Pre-Algebra Examples

$\begin{array}{c} x & y \\ 2 & 35 \\ 4 & 95 \\ 6 & 120 \\ 8 & 145 \\ 10 & 175 \end{array}$

Step 1

Check if the function rule is linear.

Tap for more steps...

Step 1.1

To find if the table follows a function rule, check to see if the values follow the linear form $y = a x + b$ .

$y = a x + b$

Step 1.2

Build a set of equations from the table such that $y = a x + b$ .

$35 = a (2) + b 95 = a (4) + b 120 = a (6) + b 145 = a (8) + b 175 = a (10) + b$

Step 1.3

Calculate the values of $a$ and $b$ .

Tap for more steps...

Step 1.3.1

Solve for $b$ in $35 = a (2) + b$ .

Tap for more steps...

Step 1.3.1.1

Rewrite the equation as $a (2) + b = 35$ .

$a (2) + b = 35$

$95 = a (4) + b$

$120 = a (6) + b$

$145 = a (8) + b$

$175 = a (10) + b$

Step 1.3.1.2

Move $2$ to the left of $a$ .

$2 a + b = 35$

$95 = a (4) + b$

$120 = a (6) + b$

$145 = a (8) + b$

$175 = a (10) + b$

Step 1.3.1.3

Subtract $2 a$ from both sides of the equation.

$b = 35 - 2 a$

$95 = a (4) + b$

$120 = a (6) + b$

$145 = a (8) + b$

$175 = a (10) + b$

$b = 35 - 2 a$

$95 = a (4) + b$

$120 = a (6) + b$

$145 = a (8) + b$

$175 = a (10) + b$

Step 1.3.2

Replace all occurrences of $b$ with $35 - 2 a$ in each equation.

Tap for more steps...

Step 1.3.2.1

Replace all occurrences of $b$ in $95 = a (4) + b$ with $35 - 2 a$ .

$95 = a (4) + 35 - 2 a$

$b = 35 - 2 a$

$120 = a (6) + b$

$145 = a (8) + b$

$175 = a (10) + b$

Step 1.3.2.2

Simplify $95 = a (4) + 35 - 2 a$ .

Tap for more steps...

Step 1.3.2.2.1

Simplify the left side.

Tap for more steps...

Step 1.3.2.2.1.1

Remove parentheses.

$95 = a (4) + 35 - 2 a$

$b = 35 - 2 a$

$120 = a (6) + b$

$145 = a (8) + b$

$175 = a (10) + b$

$95 = a (4) + 35 - 2 a$

$b = 35 - 2 a$

$120 = a (6) + b$

$145 = a (8) + b$

$175 = a (10) + b$

Step 1.3.2.2.2

Simplify the right side.

Tap for more steps...

Step 1.3.2.2.2.1

Simplify $a (4) + 35 - 2 a$ .

Tap for more steps...

Step 1.3.2.2.2.1.1

Move $4$ to the left of $a$ .

$95 = 4 a + 35 - 2 a$

$b = 35 - 2 a$

$120 = a (6) + b$

$145 = a (8) + b$

$175 = a (10) + b$

Step 1.3.2.2.2.1.2

Subtract $2 a$ from $4 a$ .

$95 = 2 a + 35$

$b = 35 - 2 a$

$120 = a (6) + b$

$145 = a (8) + b$

$175 = a (10) + b$

$95 = 2 a + 35$

$b = 35 - 2 a$

$120 = a (6) + b$

$145 = a (8) + b$

$175 = a (10) + b$

$95 = 2 a + 35$

$b = 35 - 2 a$

$120 = a (6) + b$

$145 = a (8) + b$

$175 = a (10) + b$

$95 = 2 a + 35$

$b = 35 - 2 a$

$120 = a (6) + b$

$145 = a (8) + b$

$175 = a (10) + b$

Step 1.3.2.3

Replace all occurrences of $b$ in $120 = a (6) + b$ with $35 - 2 a$ .

$120 = a (6) + 35 - 2 a$

$95 = 2 a + 35$

$b = 35 - 2 a$

$145 = a (8) + b$

$175 = a (10) + b$

Step 1.3.2.4

Simplify $120 = a (6) + 35 - 2 a$ .

Tap for more steps...

Step 1.3.2.4.1

Simplify the left side.

Tap for more steps...

Step 1.3.2.4.1.1

Remove parentheses.

$120 = a (6) + 35 - 2 a$

$95 = 2 a + 35$

$b = 35 - 2 a$

$145 = a (8) + b$

$175 = a (10) + b$

$120 = a (6) + 35 - 2 a$

$95 = 2 a + 35$

$b = 35 - 2 a$

$145 = a (8) + b$

$175 = a (10) + b$

Step 1.3.2.4.2

Simplify the right side.

Tap for more steps...

Step 1.3.2.4.2.1

Simplify $a (6) + 35 - 2 a$ .

Tap for more steps...

Step 1.3.2.4.2.1.1

Move $6$ to the left of $a$ .

$120 = 6 a + 35 - 2 a$

$95 = 2 a + 35$

$b = 35 - 2 a$

$145 = a (8) + b$

$175 = a (10) + b$

Step 1.3.2.4.2.1.2

Subtract $2 a$ from $6 a$ .

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

$145 = a (8) + b$

$175 = a (10) + b$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

$145 = a (8) + b$

$175 = a (10) + b$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

$145 = a (8) + b$

$175 = a (10) + b$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

$145 = a (8) + b$

$175 = a (10) + b$

Step 1.3.2.5

Replace all occurrences of $b$ in $145 = a (8) + b$ with $35 - 2 a$ .

$145 = a (8) + 35 - 2 a$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

$175 = a (10) + b$

Step 1.3.2.6

Simplify $145 = a (8) + 35 - 2 a$ .

Tap for more steps...

Step 1.3.2.6.1

Simplify the left side.

Tap for more steps...

Step 1.3.2.6.1.1

Remove parentheses.

$145 = a (8) + 35 - 2 a$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

$175 = a (10) + b$

$145 = a (8) + 35 - 2 a$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

$175 = a (10) + b$

Step 1.3.2.6.2

Simplify the right side.

Tap for more steps...

Step 1.3.2.6.2.1

Simplify $a (8) + 35 - 2 a$ .

Tap for more steps...

Step 1.3.2.6.2.1.1

Move $8$ to the left of $a$ .

$145 = 8 a + 35 - 2 a$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

$175 = a (10) + b$

Step 1.3.2.6.2.1.2

Subtract $2 a$ from $8 a$ .

$145 = 6 a + 35$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

$175 = a (10) + b$

$145 = 6 a + 35$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

$175 = a (10) + b$

$145 = 6 a + 35$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

$175 = a (10) + b$

$145 = 6 a + 35$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

$175 = a (10) + b$

Step 1.3.2.7

Replace all occurrences of $b$ in $175 = a (10) + b$ with $35 - 2 a$ .

$175 = a (10) + 35 - 2 a$

$145 = 6 a + 35$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

Step 1.3.2.8

Simplify $175 = a (10) + 35 - 2 a$ .

Tap for more steps...

Step 1.3.2.8.1

Simplify the left side.

Tap for more steps...

Step 1.3.2.8.1.1

Remove parentheses.

$175 = a (10) + 35 - 2 a$

$145 = 6 a + 35$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

$175 = a (10) + 35 - 2 a$

$145 = 6 a + 35$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

Step 1.3.2.8.2

Simplify the right side.

Tap for more steps...

Step 1.3.2.8.2.1

Simplify $a (10) + 35 - 2 a$ .

Tap for more steps...

Step 1.3.2.8.2.1.1

Move $10$ to the left of $a$ .

$175 = 10 a + 35 - 2 a$

$145 = 6 a + 35$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

Step 1.3.2.8.2.1.2

Subtract $2 a$ from $10 a$ .

$175 = 8 a + 35$

$145 = 6 a + 35$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

$175 = 8 a + 35$

$145 = 6 a + 35$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

$175 = 8 a + 35$

$145 = 6 a + 35$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

$175 = 8 a + 35$

$145 = 6 a + 35$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

$175 = 8 a + 35$

$145 = 6 a + 35$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

Step 1.3.3

Solve for $a$ in $175 = 8 a + 35$ .

Tap for more steps...

Step 1.3.3.1

Rewrite the equation as $8 a + 35 = 175$ .

$8 a + 35 = 175$

$145 = 6 a + 35$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

Step 1.3.3.2

Move all terms not containing $a$ to the right side of the equation.

Tap for more steps...

Step 1.3.3.2.1

Subtract $35$ from both sides of the equation.

$8 a = 175 - 35$

$145 = 6 a + 35$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

Step 1.3.3.2.2

Subtract $35$ from $175$ .

$8 a = 140$

$145 = 6 a + 35$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

$8 a = 140$

$145 = 6 a + 35$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

Step 1.3.3.3

Divide each term in $8 a = 140$ by $8$ and simplify.

Tap for more steps...

Step 1.3.3.3.1

Divide each term in $8 a = 140$ by $8$ .

$\frac{8 a}{8} = \frac{140}{8}$

$145 = 6 a + 35$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

Step 1.3.3.3.2

Simplify the left side.

Tap for more steps...

Step 1.3.3.3.2.1

Cancel the common factor of $8$ .

Tap for more steps...

Step 1.3.3.3.2.1.1

Cancel the common factor.

$\frac{8 a}{8} = \frac{140}{8}$

$145 = 6 a + 35$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

Step 1.3.3.3.2.1.2

Divide $a$ by $1$ .

$a = \frac{140}{8}$

$145 = 6 a + 35$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

$a = \frac{140}{8}$

$145 = 6 a + 35$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

$a = \frac{140}{8}$

$145 = 6 a + 35$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

Step 1.3.3.3.3

Simplify the right side.

Tap for more steps...

Step 1.3.3.3.3.1

Cancel the common factor of $140$ and $8$ .

Tap for more steps...

Step 1.3.3.3.3.1.1

Factor $4$ out of $140$ .

$a = \frac{4 (35)}{8}$

$145 = 6 a + 35$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

Step 1.3.3.3.3.1.2

Cancel the common factors.

Tap for more steps...

Step 1.3.3.3.3.1.2.1

Factor $4$ out of $8$ .

$a = \frac{4 \cdot 35}{4 \cdot 2}$

$145 = 6 a + 35$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

Step 1.3.3.3.3.1.2.2

Cancel the common factor.

$a = \frac{4 \cdot 35}{4 \cdot 2}$

$145 = 6 a + 35$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

Step 1.3.3.3.3.1.2.3

Rewrite the expression.

$a = \frac{35}{2}$

$145 = 6 a + 35$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

$a = \frac{35}{2}$

$145 = 6 a + 35$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

$a = \frac{35}{2}$

$145 = 6 a + 35$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

$a = \frac{35}{2}$

$145 = 6 a + 35$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

$a = \frac{35}{2}$

$145 = 6 a + 35$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

$a = \frac{35}{2}$

$145 = 6 a + 35$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

Step 1.3.4

Replace all occurrences of $a$ with $\frac{35}{2}$ in each equation.

Tap for more steps...

Step 1.3.4.1

Replace all occurrences of $a$ in $145 = 6 a + 35$ with $\frac{35}{2}$ .

$145 = 6 (\frac{35}{2}) + 35$

$a = \frac{35}{2}$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

Step 1.3.4.2

Simplify the right side.

Tap for more steps...

Step 1.3.4.2.1

Simplify $6 (\frac{35}{2}) + 35$ .

Tap for more steps...

Step 1.3.4.2.1.1

Simplify each term.

Tap for more steps...

Step 1.3.4.2.1.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.3.4.2.1.1.1.1

Factor $2$ out of $6$ .

$145 = 2 (3) (\frac{35}{2}) + 35$

$a = \frac{35}{2}$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

Step 1.3.4.2.1.1.1.2

Cancel the common factor.

$145 = 2 \cdot (3 (\frac{35}{2})) + 35$

$a = \frac{35}{2}$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

Step 1.3.4.2.1.1.1.3

Rewrite the expression.

$145 = 3 \cdot 35 + 35$

$a = \frac{35}{2}$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

$145 = 3 \cdot 35 + 35$

$a = \frac{35}{2}$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

Step 1.3.4.2.1.1.2

Multiply $3$ by $35$ .

$145 = 105 + 35$

$a = \frac{35}{2}$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

$145 = 105 + 35$

$a = \frac{35}{2}$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

Step 1.3.4.2.1.2

Add $105$ and $35$ .

$145 = 140$

$a = \frac{35}{2}$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

$145 = 140$

$a = \frac{35}{2}$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

$145 = 140$

$a = \frac{35}{2}$

$120 = 4 a + 35$

$95 = 2 a + 35$

$b = 35 - 2 a$

Step 1.3.4.3

Replace all occurrences of $a$ in $120 = 4 a + 35$ with $\frac{35}{2}$ .

$120 = 4 (\frac{35}{2}) + 35$

$145 = 140$

$a = \frac{35}{2}$

$95 = 2 a + 35$

$b = 35 - 2 a$

Step 1.3.4.4

Simplify the right side.

Tap for more steps...

Step 1.3.4.4.1

Simplify $4 (\frac{35}{2}) + 35$ .

Tap for more steps...

Step 1.3.4.4.1.1

Simplify each term.

Tap for more steps...

Step 1.3.4.4.1.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.3.4.4.1.1.1.1

Factor $2$ out of $4$ .

$120 = 2 (2) (\frac{35}{2}) + 35$

$145 = 140$

$a = \frac{35}{2}$

$95 = 2 a + 35$

$b = 35 - 2 a$

Step 1.3.4.4.1.1.1.2

Cancel the common factor.

$120 = 2 \cdot (2 (\frac{35}{2})) + 35$

$145 = 140$

$a = \frac{35}{2}$

$95 = 2 a + 35$

$b = 35 - 2 a$

Step 1.3.4.4.1.1.1.3

Rewrite the expression.

$120 = 2 \cdot 35 + 35$

$145 = 140$

$a = \frac{35}{2}$

$95 = 2 a + 35$

$b = 35 - 2 a$

$120 = 2 \cdot 35 + 35$

$145 = 140$

$a = \frac{35}{2}$

$95 = 2 a + 35$

$b = 35 - 2 a$

Step 1.3.4.4.1.1.2

Multiply $2$ by $35$ .

$120 = 70 + 35$

$145 = 140$

$a = \frac{35}{2}$

$95 = 2 a + 35$

$b = 35 - 2 a$

$120 = 70 + 35$

$145 = 140$

$a = \frac{35}{2}$

$95 = 2 a + 35$

$b = 35 - 2 a$

Step 1.3.4.4.1.2

Add $70$ and $35$ .

$120 = 105$

$145 = 140$

$a = \frac{35}{2}$

$95 = 2 a + 35$

$b = 35 - 2 a$

$120 = 105$

$145 = 140$

$a = \frac{35}{2}$

$95 = 2 a + 35$

$b = 35 - 2 a$

$120 = 105$

$145 = 140$

$a = \frac{35}{2}$

$95 = 2 a + 35$

$b = 35 - 2 a$

Step 1.3.4.5

Replace all occurrences of $a$ in $95 = 2 a + 35$ with $\frac{35}{2}$ .

$95 = 2 (\frac{35}{2}) + 35$

$120 = 105$

$145 = 140$

$a = \frac{35}{2}$

$b = 35 - 2 a$

Step 1.3.4.6

Simplify the right side.

Tap for more steps...

Step 1.3.4.6.1

Simplify $2 (\frac{35}{2}) + 35$ .

Tap for more steps...

Step 1.3.4.6.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.3.4.6.1.1.1

Cancel the common factor.

$95 = 2 (\frac{35}{2}) + 35$

$120 = 105$

$145 = 140$

$a = \frac{35}{2}$

$b = 35 - 2 a$

Step 1.3.4.6.1.1.2

Rewrite the expression.

$95 = 35 + 35$

$120 = 105$

$145 = 140$

$a = \frac{35}{2}$

$b = 35 - 2 a$

$95 = 35 + 35$

$120 = 105$

$145 = 140$

$a = \frac{35}{2}$

$b = 35 - 2 a$

Step 1.3.4.6.1.2

Add $35$ and $35$ .

$95 = 70$

$120 = 105$

$145 = 140$

$a = \frac{35}{2}$

$b = 35 - 2 a$

$95 = 70$

$120 = 105$

$145 = 140$

$a = \frac{35}{2}$

$b = 35 - 2 a$

$95 = 70$

$120 = 105$

$145 = 140$

$a = \frac{35}{2}$

$b = 35 - 2 a$

Step 1.3.4.7

Replace all occurrences of $a$ in $b = 35 - 2 a$ with $\frac{35}{2}$ .

$b = 35 - 2 (\frac{35}{2})$

$95 = 70$

$120 = 105$

$145 = 140$

$a = \frac{35}{2}$

Step 1.3.4.8

Simplify the right side.

Tap for more steps...

Step 1.3.4.8.1

Simplify $35 - 2 (\frac{35}{2})$ .

Tap for more steps...

Step 1.3.4.8.1.1

Simplify each term.

Tap for more steps...

Step 1.3.4.8.1.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.3.4.8.1.1.1.1

Factor $2$ out of $- 2$ .

$b = 35 + 2 (- 1) (\frac{35}{2})$

$95 = 70$

$120 = 105$

$145 = 140$

$a = \frac{35}{2}$

Step 1.3.4.8.1.1.1.2

Cancel the common factor.

$b = 35 + 2 \cdot (- 1 (\frac{35}{2}))$

$95 = 70$

$120 = 105$

$145 = 140$

$a = \frac{35}{2}$

Step 1.3.4.8.1.1.1.3

Rewrite the expression.

$b = 35 - 1 \cdot 35$

$95 = 70$

$120 = 105$

$145 = 140$

$a = \frac{35}{2}$

$b = 35 - 1 \cdot 35$

$95 = 70$

$120 = 105$

$145 = 140$

$a = \frac{35}{2}$

Step 1.3.4.8.1.1.2

Multiply $- 1$ by $35$ .

$b = 35 - 35$

$95 = 70$

$120 = 105$

$145 = 140$

$a = \frac{35}{2}$

$b = 35 - 35$

$95 = 70$

$120 = 105$

$145 = 140$

$a = \frac{35}{2}$

Step 1.3.4.8.1.2

Subtract $35$ from $35$ .

$b = 0$

$95 = 70$

$120 = 105$

$145 = 140$

$a = \frac{35}{2}$

$b = 0$

$95 = 70$

$120 = 105$

$145 = 140$

$a = \frac{35}{2}$

$b = 0$

$95 = 70$

$120 = 105$

$145 = 140$

$a = \frac{35}{2}$

$b = 0$

$95 = 70$

$120 = 105$

$145 = 140$

$a = \frac{35}{2}$

Step 1.3.5

Since $95 = 70$ is not true, there is no solution.

No solution

Step 1.4

Since $y \neq y$ for the corresponding $x$ values, the function is not linear.

The function is not linear

Step 2

Check if the function rule is quadratic.

Tap for more steps...

Step 2.1

To find if the table follows a function rule, check whether the function rule could follow the form $y = a x^{2} + b x + c$ .

$y = a x^{2} + b x + c$

Step 2.2

Build a set of $3$ equations from the table such that $y = a x^{2} + b x + c$ .

Step 2.3

Calculate the values of $a$ , $b$ , and $c$ .

Tap for more steps...

Step 2.3.1

Solve for $c$ in $35 = a \cdot 2^{2} + b (2) + c$ .

Tap for more steps...

Step 2.3.1.1

Rewrite the equation as $a \cdot 2^{2} + b (2) + c = 35$ .

$a \cdot 2^{2} + b (2) + c = 35$

$95 = a \cdot 4^{2} + b (4) + c$

$120 = a \cdot 6^{2} + b (6) + c$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

Step 2.3.1.2

Simplify each term.

Tap for more steps...

Step 2.3.1.2.1

Raise $2$ to the power of $2$ .

$a \cdot 4 + b (2) + c = 35$

$95 = a \cdot 4^{2} + b (4) + c$

$120 = a \cdot 6^{2} + b (6) + c$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

Step 2.3.1.2.2

Move $4$ to the left of $a$ .

$4 \cdot a + b (2) + c = 35$

$95 = a \cdot 4^{2} + b (4) + c$

$120 = a \cdot 6^{2} + b (6) + c$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

Step 2.3.1.2.3

Move $2$ to the left of $b$ .

$4 a + 2 b + c = 35$

$95 = a \cdot 4^{2} + b (4) + c$

$120 = a \cdot 6^{2} + b (6) + c$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

$4 a + 2 b + c = 35$

$95 = a \cdot 4^{2} + b (4) + c$

$120 = a \cdot 6^{2} + b (6) + c$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

Step 2.3.1.3

Move all terms not containing $c$ to the right side of the equation.

Tap for more steps...

Step 2.3.1.3.1

Subtract $4 a$ from both sides of the equation.

$2 b + c = 35 - 4 a$

$95 = a \cdot 4^{2} + b (4) + c$

$120 = a \cdot 6^{2} + b (6) + c$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

Step 2.3.1.3.2

Subtract $2 b$ from both sides of the equation.

$c = 35 - 4 a - 2 b$

$95 = a \cdot 4^{2} + b (4) + c$

$120 = a \cdot 6^{2} + b (6) + c$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

$c = 35 - 4 a - 2 b$

$95 = a \cdot 4^{2} + b (4) + c$

$120 = a \cdot 6^{2} + b (6) + c$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

$c = 35 - 4 a - 2 b$

$95 = a \cdot 4^{2} + b (4) + c$

$120 = a \cdot 6^{2} + b (6) + c$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

Step 2.3.2

Replace all occurrences of $c$ with $35 - 4 a - 2 b$ in each equation.

Tap for more steps...

Step 2.3.2.1

Replace all occurrences of $c$ in $95 = a \cdot 4^{2} + b (4) + c$ with $35 - 4 a - 2 b$ .

$95 = a \cdot 4^{2} + b (4) + 35 - 4 a - 2 b$

$c = 35 - 4 a - 2 b$

$120 = a \cdot 6^{2} + b (6) + c$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

Step 2.3.2.2

Simplify $95 = a \cdot 4^{2} + b (4) + 35 - 4 a - 2 b$ .

Tap for more steps...

Step 2.3.2.2.1

Simplify the left side.

Tap for more steps...

Step 2.3.2.2.1.1

Remove parentheses.

$95 = a \cdot 4^{2} + b (4) + 35 - 4 a - 2 b$

$c = 35 - 4 a - 2 b$

$120 = a \cdot 6^{2} + b (6) + c$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

$95 = a \cdot 4^{2} + b (4) + 35 - 4 a - 2 b$

$c = 35 - 4 a - 2 b$

$120 = a \cdot 6^{2} + b (6) + c$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

Step 2.3.2.2.2

Simplify the right side.

Tap for more steps...

Step 2.3.2.2.2.1

Simplify $a \cdot 4^{2} + b (4) + 35 - 4 a - 2 b$ .

Tap for more steps...

Step 2.3.2.2.2.1.1

Simplify each term.

Tap for more steps...

Step 2.3.2.2.2.1.1.1

Raise $4$ to the power of $2$ .

$95 = a \cdot 16 + b (4) + 35 - 4 a - 2 b$

$c = 35 - 4 a - 2 b$

$120 = a \cdot 6^{2} + b (6) + c$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

Step 2.3.2.2.2.1.1.2

Move $16$ to the left of $a$ .

$95 = 16 \cdot a + b (4) + 35 - 4 a - 2 b$

$c = 35 - 4 a - 2 b$

$120 = a \cdot 6^{2} + b (6) + c$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

Step 2.3.2.2.2.1.1.3

Move $4$ to the left of $b$ .

$95 = 16 a + 4 b + 35 - 4 a - 2 b$

$c = 35 - 4 a - 2 b$

$120 = a \cdot 6^{2} + b (6) + c$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

$95 = 16 a + 4 b + 35 - 4 a - 2 b$

$c = 35 - 4 a - 2 b$

$120 = a \cdot 6^{2} + b (6) + c$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

Step 2.3.2.2.2.1.2

Simplify by adding terms.

Tap for more steps...

Step 2.3.2.2.2.1.2.1

Subtract $4 a$ from $16 a$ .

$95 = 12 a + 4 b + 35 - 2 b$

$c = 35 - 4 a - 2 b$

$120 = a \cdot 6^{2} + b (6) + c$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

Step 2.3.2.2.2.1.2.2

Subtract $2 b$ from $4 b$ .

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$120 = a \cdot 6^{2} + b (6) + c$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$120 = a \cdot 6^{2} + b (6) + c$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$120 = a \cdot 6^{2} + b (6) + c$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$120 = a \cdot 6^{2} + b (6) + c$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$120 = a \cdot 6^{2} + b (6) + c$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

Step 2.3.2.3

Replace all occurrences of $c$ in $120 = a \cdot 6^{2} + b (6) + c$ with $35 - 4 a - 2 b$ .

$120 = a \cdot 6^{2} + b (6) + 35 - 4 a - 2 b$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

Step 2.3.2.4

Simplify $120 = a \cdot 6^{2} + b (6) + 35 - 4 a - 2 b$ .

Tap for more steps...

Step 2.3.2.4.1

Simplify the left side.

Tap for more steps...

Step 2.3.2.4.1.1

Remove parentheses.

$120 = a \cdot 6^{2} + b (6) + 35 - 4 a - 2 b$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

$120 = a \cdot 6^{2} + b (6) + 35 - 4 a - 2 b$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

Step 2.3.2.4.2

Simplify the right side.

Tap for more steps...

Step 2.3.2.4.2.1

Simplify $a \cdot 6^{2} + b (6) + 35 - 4 a - 2 b$ .

Tap for more steps...

Step 2.3.2.4.2.1.1

Simplify each term.

Tap for more steps...

Step 2.3.2.4.2.1.1.1

Raise $6$ to the power of $2$ .

$120 = a \cdot 36 + b (6) + 35 - 4 a - 2 b$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

Step 2.3.2.4.2.1.1.2

Move $36$ to the left of $a$ .

$120 = 36 \cdot a + b (6) + 35 - 4 a - 2 b$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

Step 2.3.2.4.2.1.1.3

Move $6$ to the left of $b$ .

$120 = 36 a + 6 b + 35 - 4 a - 2 b$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

$120 = 36 a + 6 b + 35 - 4 a - 2 b$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

Step 2.3.2.4.2.1.2

Simplify by adding terms.

Tap for more steps...

Step 2.3.2.4.2.1.2.1

Subtract $4 a$ from $36 a$ .

$120 = 32 a + 6 b + 35 - 2 b$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

Step 2.3.2.4.2.1.2.2

Subtract $2 b$ from $6 b$ .

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$145 = a \cdot 8^{2} + b (8) + c$

$175 = a \cdot 10^{2} + b (10) + c$

Step 2.3.2.5

Replace all occurrences of $c$ in $145 = a \cdot 8^{2} + b (8) + c$ with $35 - 4 a - 2 b$ .

$145 = a \cdot 8^{2} + b (8) + 35 - 4 a - 2 b$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$175 = a \cdot 10^{2} + b (10) + c$

Step 2.3.2.6

Simplify $145 = a \cdot 8^{2} + b (8) + 35 - 4 a - 2 b$ .

Tap for more steps...

Step 2.3.2.6.1

Simplify the left side.

Tap for more steps...

Step 2.3.2.6.1.1

Remove parentheses.

$145 = a \cdot 8^{2} + b (8) + 35 - 4 a - 2 b$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$175 = a \cdot 10^{2} + b (10) + c$

$145 = a \cdot 8^{2} + b (8) + 35 - 4 a - 2 b$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$175 = a \cdot 10^{2} + b (10) + c$

Step 2.3.2.6.2

Simplify the right side.

Tap for more steps...

Step 2.3.2.6.2.1

Simplify $a \cdot 8^{2} + b (8) + 35 - 4 a - 2 b$ .

Tap for more steps...

Step 2.3.2.6.2.1.1

Simplify each term.

Tap for more steps...

Step 2.3.2.6.2.1.1.1

Raise $8$ to the power of $2$ .

$145 = a \cdot 64 + b (8) + 35 - 4 a - 2 b$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$175 = a \cdot 10^{2} + b (10) + c$

Step 2.3.2.6.2.1.1.2

Move $64$ to the left of $a$ .

$145 = 64 \cdot a + b (8) + 35 - 4 a - 2 b$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$175 = a \cdot 10^{2} + b (10) + c$

Step 2.3.2.6.2.1.1.3

Move $8$ to the left of $b$ .

$145 = 64 a + 8 b + 35 - 4 a - 2 b$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$175 = a \cdot 10^{2} + b (10) + c$

$145 = 64 a + 8 b + 35 - 4 a - 2 b$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$175 = a \cdot 10^{2} + b (10) + c$

Step 2.3.2.6.2.1.2

Simplify by adding terms.

Tap for more steps...

Step 2.3.2.6.2.1.2.1

Subtract $4 a$ from $64 a$ .

$145 = 60 a + 8 b + 35 - 2 b$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$175 = a \cdot 10^{2} + b (10) + c$

Step 2.3.2.6.2.1.2.2

Subtract $2 b$ from $8 b$ .

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$175 = a \cdot 10^{2} + b (10) + c$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$175 = a \cdot 10^{2} + b (10) + c$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$175 = a \cdot 10^{2} + b (10) + c$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$175 = a \cdot 10^{2} + b (10) + c$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$175 = a \cdot 10^{2} + b (10) + c$

Step 2.3.2.7

Replace all occurrences of $c$ in $175 = a \cdot 10^{2} + b (10) + c$ with $35 - 4 a - 2 b$ .

$175 = a \cdot 10^{2} + b (10) + 35 - 4 a - 2 b$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.2.8

Simplify $175 = a \cdot 10^{2} + b (10) + 35 - 4 a - 2 b$ .

Tap for more steps...

Step 2.3.2.8.1

Simplify the left side.

Tap for more steps...

Step 2.3.2.8.1.1

Remove parentheses.

$175 = a \cdot 10^{2} + b (10) + 35 - 4 a - 2 b$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$175 = a \cdot 10^{2} + b (10) + 35 - 4 a - 2 b$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.2.8.2

Simplify the right side.

Tap for more steps...

Step 2.3.2.8.2.1

Simplify $a \cdot 10^{2} + b (10) + 35 - 4 a - 2 b$ .

Tap for more steps...

Step 2.3.2.8.2.1.1

Simplify each term.

Tap for more steps...

Step 2.3.2.8.2.1.1.1

Raise $10$ to the power of $2$ .

$175 = a \cdot 100 + b (10) + 35 - 4 a - 2 b$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.2.8.2.1.1.2

Move $100$ to the left of $a$ .

$175 = 100 \cdot a + b (10) + 35 - 4 a - 2 b$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.2.8.2.1.1.3

Move $10$ to the left of $b$ .

$175 = 100 a + 10 b + 35 - 4 a - 2 b$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$175 = 100 a + 10 b + 35 - 4 a - 2 b$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.2.8.2.1.2

Simplify by adding terms.

Tap for more steps...

Step 2.3.2.8.2.1.2.1

Subtract $4 a$ from $100 a$ .

$175 = 96 a + 10 b + 35 - 2 b$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.2.8.2.1.2.2

Subtract $2 b$ from $10 b$ .

$175 = 96 a + 8 b + 35$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$175 = 96 a + 8 b + 35$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$175 = 96 a + 8 b + 35$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$175 = 96 a + 8 b + 35$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$175 = 96 a + 8 b + 35$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$175 = 96 a + 8 b + 35$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.3

Solve for $a$ in $175 = 96 a + 8 b + 35$ .

Tap for more steps...

Step 2.3.3.1

Rewrite the equation as $96 a + 8 b + 35 = 175$ .

$96 a + 8 b + 35 = 175$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.3.2

Move all terms not containing $a$ to the right side of the equation.

Tap for more steps...

Step 2.3.3.2.1

Subtract $8 b$ from both sides of the equation.

$96 a + 35 = 175 - 8 b$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.3.2.2

Subtract $35$ from both sides of the equation.

$96 a = 175 - 8 b - 35$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.3.2.3

Subtract $35$ from $175$ .

$96 a = - 8 b + 140$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$96 a = - 8 b + 140$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.3.3

Divide each term in $96 a = - 8 b + 140$ by $96$ and simplify.

Tap for more steps...

Step 2.3.3.3.1

Divide each term in $96 a = - 8 b + 140$ by $96$ .

$\frac{96 a}{96} = \frac{- 8 b}{96} + \frac{140}{96}$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.3.3.2

Simplify the left side.

Tap for more steps...

Step 2.3.3.3.2.1

Cancel the common factor of $96$ .

Tap for more steps...

Step 2.3.3.3.2.1.1

Cancel the common factor.

$\frac{96 a}{96} = \frac{- 8 b}{96} + \frac{140}{96}$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.3.3.2.1.2

Divide $a$ by $1$ .

$a = \frac{- 8 b}{96} + \frac{140}{96}$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$a = \frac{- 8 b}{96} + \frac{140}{96}$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$a = \frac{- 8 b}{96} + \frac{140}{96}$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.3.3.3

Simplify the right side.

Tap for more steps...

Step 2.3.3.3.3.1

Simplify each term.

Tap for more steps...

Step 2.3.3.3.3.1.1

Cancel the common factor of $- 8$ and $96$ .

Tap for more steps...

Step 2.3.3.3.3.1.1.1

Factor $8$ out of $- 8 b$ .

$a = \frac{8 (- b)}{96} + \frac{140}{96}$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.3.3.3.1.1.2

Cancel the common factors.

Tap for more steps...

Step 2.3.3.3.3.1.1.2.1

Factor $8$ out of $96$ .

$a = \frac{8 (- b)}{8 (12)} + \frac{140}{96}$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.3.3.3.1.1.2.2

Cancel the common factor.

$a = \frac{8 (- b)}{8 \cdot 12} + \frac{140}{96}$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.3.3.3.1.1.2.3

Rewrite the expression.

$a = \frac{- b}{12} + \frac{140}{96}$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$a = \frac{- b}{12} + \frac{140}{96}$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$a = \frac{- b}{12} + \frac{140}{96}$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.3.3.3.1.2

Move the negative in front of the fraction.

$a = - \frac{b}{12} + \frac{140}{96}$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.3.3.3.1.3

Cancel the common factor of $140$ and $96$ .

Tap for more steps...

Step 2.3.3.3.3.1.3.1

Factor $4$ out of $140$ .

$a = - \frac{b}{12} + \frac{4 (35)}{96}$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.3.3.3.1.3.2

Cancel the common factors.

Tap for more steps...

Step 2.3.3.3.3.1.3.2.1

Factor $4$ out of $96$ .

$a = - \frac{b}{12} + \frac{4 \cdot 35}{4 \cdot 24}$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.3.3.3.1.3.2.2

Cancel the common factor.

$a = - \frac{b}{12} + \frac{4 \cdot 35}{4 \cdot 24}$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.3.3.3.1.3.2.3

Rewrite the expression.

$a = - \frac{b}{12} + \frac{35}{24}$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$a = - \frac{b}{12} + \frac{35}{24}$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$a = - \frac{b}{12} + \frac{35}{24}$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$a = - \frac{b}{12} + \frac{35}{24}$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$a = - \frac{b}{12} + \frac{35}{24}$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$a = - \frac{b}{12} + \frac{35}{24}$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$a = - \frac{b}{12} + \frac{35}{24}$

$145 = 60 a + 6 b + 35$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4

Replace all occurrences of $a$ with $- \frac{b}{12} + \frac{35}{24}$ in each equation.

Tap for more steps...

Step 2.3.4.1

Replace all occurrences of $a$ in $145 = 60 a + 6 b + 35$ with $- \frac{b}{12} + \frac{35}{24}$ .

$145 = 60 (- \frac{b}{12} + \frac{35}{24}) + 6 b + 35$

$a = - \frac{b}{12} + \frac{35}{24}$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.2

Simplify the right side.

Tap for more steps...

Step 2.3.4.2.1

Simplify $60 (- \frac{b}{12} + \frac{35}{24}) + 6 b + 35$ .

Tap for more steps...

Step 2.3.4.2.1.1

Simplify each term.

Tap for more steps...

Step 2.3.4.2.1.1.1

Apply the distributive property.

$145 = 60 (- \frac{b}{12}) + 60 (\frac{35}{24}) + 6 b + 35$

$a = - \frac{b}{12} + \frac{35}{24}$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.2.1.1.2

Cancel the common factor of $12$ .

Tap for more steps...

Step 2.3.4.2.1.1.2.1

Move the leading negative in $- \frac{b}{12}$ into the numerator.

$145 = 60 (\frac{- b}{12}) + 60 (\frac{35}{24}) + 6 b + 35$

$a = - \frac{b}{12} + \frac{35}{24}$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.2.1.1.2.2

Factor $12$ out of $60$ .

$145 = 12 (5) (\frac{- b}{12}) + 60 (\frac{35}{24}) + 6 b + 35$

$a = - \frac{b}{12} + \frac{35}{24}$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.2.1.1.2.3

Cancel the common factor.

$145 = 12 \cdot (5 (\frac{- b}{12})) + 60 (\frac{35}{24}) + 6 b + 35$

$a = - \frac{b}{12} + \frac{35}{24}$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.2.1.1.2.4

Rewrite the expression.

$145 = 5 (- b) + 60 (\frac{35}{24}) + 6 b + 35$

$a = - \frac{b}{12} + \frac{35}{24}$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$145 = 5 (- b) + 60 (\frac{35}{24}) + 6 b + 35$

$a = - \frac{b}{12} + \frac{35}{24}$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.2.1.1.3

Multiply $- 1$ by $5$ .

$145 = - 5 b + 60 (\frac{35}{24}) + 6 b + 35$

$a = - \frac{b}{12} + \frac{35}{24}$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.2.1.1.4

Cancel the common factor of $12$ .

Tap for more steps...

Step 2.3.4.2.1.1.4.1

Factor $12$ out of $60$ .

$145 = - 5 b + 12 (5) (\frac{35}{24}) + 6 b + 35$

$a = - \frac{b}{12} + \frac{35}{24}$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.2.1.1.4.2

Factor $12$ out of $24$ .

$145 = - 5 b + 12 \cdot (5 (\frac{35}{12 \cdot 2})) + 6 b + 35$

$a = - \frac{b}{12} + \frac{35}{24}$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.2.1.1.4.3

Cancel the common factor.

$145 = - 5 b + 12 \cdot (5 (\frac{35}{12 \cdot 2})) + 6 b + 35$

$a = - \frac{b}{12} + \frac{35}{24}$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.2.1.1.4.4

Rewrite the expression.

$145 = - 5 b + 5 (\frac{35}{2}) + 6 b + 35$

$a = - \frac{b}{12} + \frac{35}{24}$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$145 = - 5 b + 5 (\frac{35}{2}) + 6 b + 35$

$a = - \frac{b}{12} + \frac{35}{24}$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.2.1.1.5

Combine $5$ and $\frac{35}{2}$ .

$145 = - 5 b + \frac{5 \cdot 35}{2} + 6 b + 35$

$a = - \frac{b}{12} + \frac{35}{24}$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.2.1.1.6

Multiply $5$ by $35$ .

$145 = - 5 b + \frac{175}{2} + 6 b + 35$

$a = - \frac{b}{12} + \frac{35}{24}$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$145 = - 5 b + \frac{175}{2} + 6 b + 35$

$a = - \frac{b}{12} + \frac{35}{24}$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.2.1.2

Add $- 5 b$ and $6 b$ .

$145 = b + \frac{175}{2} + 35$

$a = - \frac{b}{12} + \frac{35}{24}$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.2.1.3

To write $35$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$145 = b + \frac{175}{2} + 35 \cdot \frac{2}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.2.1.4

Combine $35$ and $\frac{2}{2}$ .

$145 = b + \frac{175}{2} + \frac{35 \cdot 2}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.2.1.5

Combine the numerators over the common denominator.

$145 = b + \frac{175 + 35 \cdot 2}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.2.1.6

Simplify the numerator.

Tap for more steps...

Step 2.3.4.2.1.6.1

Multiply $35$ by $2$ .

$145 = b + \frac{175 + 70}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.2.1.6.2

Add $175$ and $70$ .

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$120 = 32 a + 4 b + 35$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.3

Replace all occurrences of $a$ in $120 = 32 a + 4 b + 35$ with $- \frac{b}{12} + \frac{35}{24}$ .

$120 = 32 (- \frac{b}{12} + \frac{35}{24}) + 4 b + 35$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.4

Simplify the right side.

Tap for more steps...

Step 2.3.4.4.1

Simplify $32 (- \frac{b}{12} + \frac{35}{24}) + 4 b + 35$ .

Tap for more steps...

Step 2.3.4.4.1.1

Simplify each term.

Tap for more steps...

Step 2.3.4.4.1.1.1

Apply the distributive property.

$120 = 32 (- \frac{b}{12}) + 32 (\frac{35}{24}) + 4 b + 35$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.4.1.1.2

Cancel the common factor of $4$ .

Tap for more steps...

Step 2.3.4.4.1.1.2.1

Move the leading negative in $- \frac{b}{12}$ into the numerator.

$120 = 32 (\frac{- b}{12}) + 32 (\frac{35}{24}) + 4 b + 35$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.4.1.1.2.2

Factor $4$ out of $32$ .

$120 = 4 (8) (\frac{- b}{12}) + 32 (\frac{35}{24}) + 4 b + 35$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.4.1.1.2.3

Factor $4$ out of $12$ .

$120 = 4 \cdot (8 (\frac{- b}{4 \cdot 3})) + 32 (\frac{35}{24}) + 4 b + 35$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.4.1.1.2.4

Cancel the common factor.

$120 = 4 \cdot (8 (\frac{- b}{4 \cdot 3})) + 32 (\frac{35}{24}) + 4 b + 35$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.4.1.1.2.5

Rewrite the expression.

$120 = 8 (\frac{- b}{3}) + 32 (\frac{35}{24}) + 4 b + 35$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$120 = 8 (\frac{- b}{3}) + 32 (\frac{35}{24}) + 4 b + 35$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.4.1.1.3

Combine $8$ and $\frac{- b}{3}$ .

$120 = \frac{8 (- b)}{3} + 32 (\frac{35}{24}) + 4 b + 35$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.4.1.1.4

Multiply $- 1$ by $8$ .

$120 = \frac{- 8 b}{3} + 32 (\frac{35}{24}) + 4 b + 35$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.4.1.1.5

Cancel the common factor of $8$ .

Tap for more steps...

Step 2.3.4.4.1.1.5.1

Factor $8$ out of $32$ .

$120 = \frac{- 8 b}{3} + 8 (4) (\frac{35}{24}) + 4 b + 35$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.4.1.1.5.2

Factor $8$ out of $24$ .

$120 = \frac{- 8 b}{3} + 8 \cdot (4 (\frac{35}{8 \cdot 3})) + 4 b + 35$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.4.1.1.5.3

Cancel the common factor.

$120 = \frac{- 8 b}{3} + 8 \cdot (4 (\frac{35}{8 \cdot 3})) + 4 b + 35$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.4.1.1.5.4

Rewrite the expression.

$120 = \frac{- 8 b}{3} + 4 (\frac{35}{3}) + 4 b + 35$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$120 = \frac{- 8 b}{3} + 4 (\frac{35}{3}) + 4 b + 35$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.4.1.1.6

Combine $4$ and $\frac{35}{3}$ .

$120 = \frac{- 8 b}{3} + \frac{4 \cdot 35}{3} + 4 b + 35$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.4.1.1.7

Multiply $4$ by $35$ .

$120 = \frac{- 8 b}{3} + \frac{140}{3} + 4 b + 35$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.4.1.1.8

Move the negative in front of the fraction.

$120 = - \frac{8 b}{3} + \frac{140}{3} + 4 b + 35$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$120 = - \frac{8 b}{3} + \frac{140}{3} + 4 b + 35$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.4.1.2

To write $4 b$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$120 = - \frac{8 b}{3} + 4 b \cdot \frac{3}{3} + \frac{140}{3} + 35$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.4.1.3

Combine $4 b$ and $\frac{3}{3}$ .

$120 = - \frac{8 b}{3} + \frac{4 b \cdot 3}{3} + \frac{140}{3} + 35$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.4.1.4

Combine the numerators over the common denominator.

$120 = \frac{- 8 b + 4 b \cdot 3}{3} + \frac{140}{3} + 35$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.4.1.5

Combine the numerators over the common denominator.

$120 = 35 + \frac{- 8 b + 4 b \cdot 3 + 140}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.4.1.6

Multiply $3$ by $4$ .

$120 = 35 + \frac{- 8 b + 12 b + 140}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.4.1.7

Add $- 8 b$ and $12 b$ .

$120 = 35 + \frac{4 b + 140}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.4.1.8

Factor $4$ out of $4 b + 140$ .

Tap for more steps...

Step 2.3.4.4.1.8.1

Factor $4$ out of $4 b$ .

$120 = 35 + \frac{4 (b) + 140}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.4.1.8.2

Factor $4$ out of $140$ .

$120 = 35 + \frac{4 b + 4 \cdot 35}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.4.1.8.3

Factor $4$ out of $4 b + 4 \cdot 35$ .

$120 = 35 + \frac{4 (b + 35)}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$120 = 35 + \frac{4 (b + 35)}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.4.1.9

To write $35$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$120 = 35 \cdot \frac{3}{3} + \frac{4 (b + 35)}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.4.1.10

Simplify terms.

Tap for more steps...

Step 2.3.4.4.1.10.1

Combine $35$ and $\frac{3}{3}$ .

$120 = \frac{35 \cdot 3}{3} + \frac{4 (b + 35)}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.4.1.10.2

Combine the numerators over the common denominator.

$120 = \frac{35 \cdot 3 + 4 (b + 35)}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$120 = \frac{35 \cdot 3 + 4 (b + 35)}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.4.1.11

Simplify the numerator.

Tap for more steps...

Step 2.3.4.4.1.11.1

Multiply $35$ by $3$ .

$120 = \frac{105 + 4 (b + 35)}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.4.1.11.2

Apply the distributive property.

$120 = \frac{105 + 4 b + 4 \cdot 35}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.4.1.11.3

Multiply $4$ by $35$ .

$120 = \frac{105 + 4 b + 140}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.4.1.11.4

Add $105$ and $140$ .

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$95 = 12 a + 2 b + 35$

$c = 35 - 4 a - 2 b$

Step 2.3.4.5

Replace all occurrences of $a$ in $95 = 12 a + 2 b + 35$ with $- \frac{b}{12} + \frac{35}{24}$ .

$95 = 12 (- \frac{b}{12} + \frac{35}{24}) + 2 b + 35$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = 35 - 4 a - 2 b$

Step 2.3.4.6

Simplify the right side.

Tap for more steps...

Step 2.3.4.6.1

Simplify $12 (- \frac{b}{12} + \frac{35}{24}) + 2 b + 35$ .

Tap for more steps...

Step 2.3.4.6.1.1

Simplify each term.

Tap for more steps...

Step 2.3.4.6.1.1.1

Apply the distributive property.

$95 = 12 (- \frac{b}{12}) + 12 (\frac{35}{24}) + 2 b + 35$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = 35 - 4 a - 2 b$

Step 2.3.4.6.1.1.2

Cancel the common factor of $12$ .

Tap for more steps...

Step 2.3.4.6.1.1.2.1

Move the leading negative in $- \frac{b}{12}$ into the numerator.

$95 = 12 (\frac{- b}{12}) + 12 (\frac{35}{24}) + 2 b + 35$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = 35 - 4 a - 2 b$

Step 2.3.4.6.1.1.2.2

Cancel the common factor.

$95 = 12 (\frac{- b}{12}) + 12 (\frac{35}{24}) + 2 b + 35$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = 35 - 4 a - 2 b$

Step 2.3.4.6.1.1.2.3

Rewrite the expression.

$95 = - b + 12 (\frac{35}{24}) + 2 b + 35$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = 35 - 4 a - 2 b$

$95 = - b + 12 (\frac{35}{24}) + 2 b + 35$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = 35 - 4 a - 2 b$

Step 2.3.4.6.1.1.3

Cancel the common factor of $12$ .

Tap for more steps...

Step 2.3.4.6.1.1.3.1

Factor $12$ out of $24$ .

$95 = - b + 12 (\frac{35}{12 (2)}) + 2 b + 35$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = 35 - 4 a - 2 b$

Step 2.3.4.6.1.1.3.2

Cancel the common factor.

$95 = - b + 12 (\frac{35}{12 \cdot 2}) + 2 b + 35$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = 35 - 4 a - 2 b$

Step 2.3.4.6.1.1.3.3

Rewrite the expression.

$95 = - b + \frac{35}{2} + 2 b + 35$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = 35 - 4 a - 2 b$

$95 = - b + \frac{35}{2} + 2 b + 35$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = 35 - 4 a - 2 b$

$95 = - b + \frac{35}{2} + 2 b + 35$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = 35 - 4 a - 2 b$

Step 2.3.4.6.1.2

Add $- b$ and $2 b$ .

$95 = b + \frac{35}{2} + 35$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = 35 - 4 a - 2 b$

Step 2.3.4.6.1.3

To write $35$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$95 = b + \frac{35}{2} + 35 \cdot \frac{2}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = 35 - 4 a - 2 b$

Step 2.3.4.6.1.4

Combine $35$ and $\frac{2}{2}$ .

$95 = b + \frac{35}{2} + \frac{35 \cdot 2}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = 35 - 4 a - 2 b$

Step 2.3.4.6.1.5

Combine the numerators over the common denominator.

$95 = b + \frac{35 + 35 \cdot 2}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = 35 - 4 a - 2 b$

Step 2.3.4.6.1.6

Simplify the numerator.

Tap for more steps...

Step 2.3.4.6.1.6.1

Multiply $35$ by $2$ .

$95 = b + \frac{35 + 70}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = 35 - 4 a - 2 b$

Step 2.3.4.6.1.6.2

Add $35$ and $70$ .

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = 35 - 4 a - 2 b$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = 35 - 4 a - 2 b$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = 35 - 4 a - 2 b$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = 35 - 4 a - 2 b$

Step 2.3.4.7

Replace all occurrences of $a$ in $c = 35 - 4 a - 2 b$ with $- \frac{b}{12} + \frac{35}{24}$ .

$c = 35 - 4 (- \frac{b}{12} + \frac{35}{24}) - 2 b$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.4.8

Simplify the right side.

Tap for more steps...

Step 2.3.4.8.1

Simplify $35 - 4 (- \frac{b}{12} + \frac{35}{24}) - 2 b$ .

Tap for more steps...

Step 2.3.4.8.1.1

Simplify each term.

Tap for more steps...

Step 2.3.4.8.1.1.1

Apply the distributive property.

$c = 35 - 4 (- \frac{b}{12}) - 4 (\frac{35}{24}) - 2 b$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.4.8.1.1.2

Cancel the common factor of $4$ .

Tap for more steps...

Step 2.3.4.8.1.1.2.1

Move the leading negative in $- \frac{b}{12}$ into the numerator.

$c = 35 - 4 \frac{- b}{12} - 4 (\frac{35}{24}) - 2 b$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.4.8.1.1.2.2

Factor $4$ out of $- 4$ .

$c = 35 + 4 (- 1) (\frac{- b}{12}) - 4 (\frac{35}{24}) - 2 b$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.4.8.1.1.2.3

Factor $4$ out of $12$ .

$c = 35 + 4 \cdot (- 1 \frac{- b}{4 \cdot 3}) - 4 (\frac{35}{24}) - 2 b$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.4.8.1.1.2.4

Cancel the common factor.

$c = 35 + 4 \cdot (- 1 \frac{- b}{4 \cdot 3}) - 4 (\frac{35}{24}) - 2 b$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.4.8.1.1.2.5

Rewrite the expression.

$c = 35 - 1 \frac{- b}{3} - 4 (\frac{35}{24}) - 2 b$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = 35 - 1 \frac{- b}{3} - 4 (\frac{35}{24}) - 2 b$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.4.8.1.1.3

Cancel the common factor of $4$ .

Tap for more steps...

Step 2.3.4.8.1.1.3.1

Factor $4$ out of $- 4$ .

$c = 35 - 1 \frac{- b}{3} + 4 (- 1) (\frac{35}{24}) - 2 b$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.4.8.1.1.3.2

Factor $4$ out of $24$ .

$c = 35 - 1 \frac{- b}{3} + 4 \cdot (- 1 \frac{35}{4 \cdot 6}) - 2 b$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.4.8.1.1.3.3

Cancel the common factor.

$c = 35 - 1 \frac{- b}{3} + 4 \cdot (- 1 \frac{35}{4 \cdot 6}) - 2 b$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.4.8.1.1.3.4

Rewrite the expression.

$c = 35 - 1 \frac{- b}{3} - 1 (\frac{35}{6}) - 2 b$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = 35 - 1 \frac{- b}{3} - 1 (\frac{35}{6}) - 2 b$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.4.8.1.1.4

Simplify each term.

Tap for more steps...

Step 2.3.4.8.1.1.4.1

Move the negative in front of the fraction.

$c = 35 - 1 (- \frac{b}{3}) - 1 (\frac{35}{6}) - 2 b$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.4.8.1.1.4.2

Multiply $- 1 (- \frac{b}{3})$ .

Tap for more steps...

Step 2.3.4.8.1.1.4.2.1

Multiply $- 1$ by $- 1$ .

$c = 35 + 1 (\frac{b}{3}) - 1 (\frac{35}{6}) - 2 b$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.4.8.1.1.4.2.2

Multiply $\frac{b}{3}$ by $1$ .

$c = 35 + \frac{b}{3} - 1 (\frac{35}{6}) - 2 b$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = 35 + \frac{b}{3} - 1 (\frac{35}{6}) - 2 b$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.4.8.1.1.4.3

Rewrite $- 1 (\frac{35}{6})$ as $- (\frac{35}{6})$ .

$c = 35 + \frac{b}{3} - \frac{35}{6} - 2 b$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = 35 + \frac{b}{3} - \frac{35}{6} - 2 b$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = 35 + \frac{b}{3} - \frac{35}{6} - 2 b$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.4.8.1.2

To write $35$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$c = \frac{b}{3} + 35 \cdot \frac{6}{6} - \frac{35}{6} - 2 b$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.4.8.1.3

Combine $35$ and $\frac{6}{6}$ .

$c = \frac{b}{3} + \frac{35 \cdot 6}{6} - \frac{35}{6} - 2 b$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.4.8.1.4

Combine the numerators over the common denominator.

$c = \frac{b}{3} + \frac{35 \cdot 6 - 35}{6} - 2 b$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.4.8.1.5

Simplify the numerator.

Tap for more steps...

Step 2.3.4.8.1.5.1

Multiply $35$ by $6$ .

$c = \frac{b}{3} + \frac{210 - 35}{6} - 2 b$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.4.8.1.5.2

Subtract $35$ from $210$ .

$c = \frac{b}{3} + \frac{175}{6} - 2 b$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = \frac{b}{3} + \frac{175}{6} - 2 b$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.4.8.1.6

To write $- 2 b$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$c = \frac{b}{3} - 2 b \cdot \frac{3}{3} + \frac{175}{6}$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.4.8.1.7

Simplify terms.

Tap for more steps...

Step 2.3.4.8.1.7.1

Combine $- 2 b$ and $\frac{3}{3}$ .

$c = \frac{b}{3} + \frac{- 2 b \cdot 3}{3} + \frac{175}{6}$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.4.8.1.7.2

Combine the numerators over the common denominator.

$c = \frac{b - 2 b \cdot 3}{3} + \frac{175}{6}$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = \frac{b - 2 b \cdot 3}{3} + \frac{175}{6}$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.4.8.1.8

Simplify each term.

Tap for more steps...

Step 2.3.4.8.1.8.1

Simplify the numerator.

Tap for more steps...

Step 2.3.4.8.1.8.1.1

Factor $b$ out of $b - 2 b \cdot 3$ .

Tap for more steps...

Step 2.3.4.8.1.8.1.1.1

Raise $b$ to the power of $1$ .

$c = \frac{b - 2 b \cdot 3}{3} + \frac{175}{6}$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.4.8.1.8.1.1.2

Factor $b$ out of $b^{1}$ .

$c = \frac{b \cdot 1 - 2 b \cdot 3}{3} + \frac{175}{6}$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.4.8.1.8.1.1.3

Factor $b$ out of $- 2 b \cdot 3$ .

$c = \frac{b \cdot 1 + b (- 2 \cdot 3)}{3} + \frac{175}{6}$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.4.8.1.8.1.1.4

Factor $b$ out of $b \cdot 1 + b (- 2 \cdot 3)$ .

$c = \frac{b (1 - 2 \cdot 3)}{3} + \frac{175}{6}$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = \frac{b (1 - 2 \cdot 3)}{3} + \frac{175}{6}$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.4.8.1.8.1.2

Multiply $- 2$ by $3$ .

$c = \frac{b (1 - 6)}{3} + \frac{175}{6}$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.4.8.1.8.1.3

Subtract $6$ from $1$ .

$c = \frac{b \cdot - 5}{3} + \frac{175}{6}$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = \frac{b \cdot - 5}{3} + \frac{175}{6}$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.4.8.1.8.2

Move $- 5$ to the left of $b$ .

$c = \frac{- 5 \cdot b}{3} + \frac{175}{6}$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.4.8.1.8.3

Move the negative in front of the fraction.

$c = - \frac{5 b}{3} + \frac{175}{6}$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = - \frac{5 b}{3} + \frac{175}{6}$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = - \frac{5 b}{3} + \frac{175}{6}$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = - \frac{5 b}{3} + \frac{175}{6}$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = - \frac{5 b}{3} + \frac{175}{6}$

$95 = b + \frac{105}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.5

Solve for $b$ in $95 = b + \frac{105}{2}$ .

Tap for more steps...

Step 2.3.5.1

Rewrite the equation as $b + \frac{105}{2} = 95$ .

$b + \frac{105}{2} = 95$

$c = - \frac{5 b}{3} + \frac{175}{6}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.5.2

Move all terms not containing $b$ to the right side of the equation.

Tap for more steps...

Step 2.3.5.2.1

Subtract $\frac{105}{2}$ from both sides of the equation.

$b = 95 - \frac{105}{2}$

$c = - \frac{5 b}{3} + \frac{175}{6}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.5.2.2

To write $95$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$b = 95 \cdot \frac{2}{2} - \frac{105}{2}$

$c = - \frac{5 b}{3} + \frac{175}{6}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.5.2.3

Combine $95$ and $\frac{2}{2}$ .

$b = \frac{95 \cdot 2}{2} - \frac{105}{2}$

$c = - \frac{5 b}{3} + \frac{175}{6}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.5.2.4

Combine the numerators over the common denominator.

$b = \frac{95 \cdot 2 - 105}{2}$

$c = - \frac{5 b}{3} + \frac{175}{6}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.5.2.5

Simplify the numerator.

Tap for more steps...

Step 2.3.5.2.5.1

Multiply $95$ by $2$ .

$b = \frac{190 - 105}{2}$

$c = - \frac{5 b}{3} + \frac{175}{6}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.5.2.5.2

Subtract $105$ from $190$ .

$b = \frac{85}{2}$

$c = - \frac{5 b}{3} + \frac{175}{6}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$b = \frac{85}{2}$

$c = - \frac{5 b}{3} + \frac{175}{6}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$b = \frac{85}{2}$

$c = - \frac{5 b}{3} + \frac{175}{6}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$b = \frac{85}{2}$

$c = - \frac{5 b}{3} + \frac{175}{6}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.6

Replace all occurrences of $b$ with $\frac{85}{2}$ in each equation.

Tap for more steps...

Step 2.3.6.1

Replace all occurrences of $b$ in $c = - \frac{5 b}{3} + \frac{175}{6}$ with $\frac{85}{2}$ .

$c = - \frac{5 (\frac{85}{2})}{3} + \frac{175}{6}$

$b = \frac{85}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.6.2

Simplify the right side.

Tap for more steps...

Step 2.3.6.2.1

Simplify $- \frac{5 (\frac{85}{2})}{3} + \frac{175}{6}$ .

Tap for more steps...

Step 2.3.6.2.1.1

Simplify each term.

Tap for more steps...

Step 2.3.6.2.1.1.1

Combine $5$ and $\frac{85}{2}$ .

$c = - \frac{\frac{5 \cdot 85}{2}}{3} + \frac{175}{6}$

$b = \frac{85}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.6.2.1.1.2

Multiply $5$ by $85$ .

$c = - \frac{\frac{425}{2}}{3} + \frac{175}{6}$

$b = \frac{85}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.6.2.1.1.3

Multiply the numerator by the reciprocal of the denominator.

$c = - (\frac{425}{2} \cdot \frac{1}{3}) + \frac{175}{6}$

$b = \frac{85}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.6.2.1.1.4

Multiply $\frac{425}{2} \cdot \frac{1}{3}$ .

Tap for more steps...

Step 2.3.6.2.1.1.4.1

Multiply $\frac{425}{2}$ by $\frac{1}{3}$ .

$c = - \frac{425}{2 \cdot 3} + \frac{175}{6}$

$b = \frac{85}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.6.2.1.1.4.2

Multiply $2$ by $3$ .

$c = - \frac{425}{6} + \frac{175}{6}$

$b = \frac{85}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = - \frac{425}{6} + \frac{175}{6}$

$b = \frac{85}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = - \frac{425}{6} + \frac{175}{6}$

$b = \frac{85}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.6.2.1.2

Simplify terms.

Tap for more steps...

Step 2.3.6.2.1.2.1

Combine the numerators over the common denominator.

$c = \frac{- 425 + 175}{6}$

$b = \frac{85}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.6.2.1.2.2

Add $- 425$ and $175$ .

$c = \frac{- 250}{6}$

$b = \frac{85}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.6.2.1.2.3

Cancel the common factor of $- 250$ and $6$ .

Tap for more steps...

Step 2.3.6.2.1.2.3.1

Factor $2$ out of $- 250$ .

$c = \frac{2 (- 125)}{6}$

$b = \frac{85}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.6.2.1.2.3.2

Cancel the common factors.

Tap for more steps...

Step 2.3.6.2.1.2.3.2.1

Factor $2$ out of $6$ .

$c = \frac{2 \cdot - 125}{2 \cdot 3}$

$b = \frac{85}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.6.2.1.2.3.2.2

Cancel the common factor.

$c = \frac{2 \cdot - 125}{2 \cdot 3}$

$b = \frac{85}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.6.2.1.2.3.2.3

Rewrite the expression.

$c = \frac{- 125}{3}$

$b = \frac{85}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = \frac{- 125}{3}$

$b = \frac{85}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = \frac{- 125}{3}$

$b = \frac{85}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.6.2.1.2.4

Move the negative in front of the fraction.

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

$120 = \frac{4 b + 245}{3}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.6.3

Replace all occurrences of $b$ in $120 = \frac{4 b + 245}{3}$ with $\frac{85}{2}$ .

$120 = \frac{4 (\frac{85}{2}) + 245}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.6.4

Simplify the right side.

Tap for more steps...

Step 2.3.6.4.1

Simplify the numerator.

Tap for more steps...

Step 2.3.6.4.1.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.3.6.4.1.1.1

Factor $2$ out of $4$ .

$120 = \frac{2 (2) (\frac{85}{2}) + 245}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.6.4.1.1.2

Cancel the common factor.

$120 = \frac{2 \cdot (2 (\frac{85}{2})) + 245}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.6.4.1.1.3

Rewrite the expression.

$120 = \frac{2 \cdot 85 + 245}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$120 = \frac{2 \cdot 85 + 245}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.6.4.1.2

Multiply $2$ by $85$ .

$120 = \frac{170 + 245}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.6.4.1.3

Add $170$ and $245$ .

$120 = \frac{415}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$120 = \frac{415}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$120 = \frac{415}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

$145 = b + \frac{245}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.6.5

Replace all occurrences of $b$ in $145 = b + \frac{245}{2}$ with $\frac{85}{2}$ .

$145 = (\frac{85}{2}) + \frac{245}{2}$

$120 = \frac{415}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.6.6

Simplify the right side.

Tap for more steps...

Step 2.3.6.6.1

Simplify $(\frac{85}{2}) + \frac{245}{2}$ .

Tap for more steps...

Step 2.3.6.6.1.1

Combine the numerators over the common denominator.

$145 = \frac{85 + 245}{2}$

$120 = \frac{415}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.6.6.1.2

Simplify the expression.

Tap for more steps...

Step 2.3.6.6.1.2.1

Add $85$ and $245$ .

$145 = \frac{330}{2}$

$120 = \frac{415}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.6.6.1.2.2

Divide $330$ by $2$ .

$145 = 165$

$120 = \frac{415}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$145 = 165$

$120 = \frac{415}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$145 = 165$

$120 = \frac{415}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

$145 = 165$

$120 = \frac{415}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

$a = - \frac{b}{12} + \frac{35}{24}$

Step 2.3.6.7

Replace all occurrences of $b$ in $a = - \frac{b}{12} + \frac{35}{24}$ with $\frac{85}{2}$ .

$a = - \frac{\frac{85}{2}}{12} + \frac{35}{24}$

$145 = 165$

$120 = \frac{415}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

Step 2.3.6.8

Simplify the right side.

Tap for more steps...

Step 2.3.6.8.1

Simplify $- \frac{\frac{85}{2}}{12} + \frac{35}{24}$ .

Tap for more steps...

Step 2.3.6.8.1.1

Simplify each term.

Tap for more steps...

Step 2.3.6.8.1.1.1

Multiply the numerator by the reciprocal of the denominator.

$a = - (\frac{85}{2} \cdot \frac{1}{12}) + \frac{35}{24}$

$145 = 165$

$120 = \frac{415}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

Step 2.3.6.8.1.1.2

Multiply $\frac{85}{2} \cdot \frac{1}{12}$ .

Tap for more steps...

Step 2.3.6.8.1.1.2.1

Multiply $\frac{85}{2}$ by $\frac{1}{12}$ .

$a = - \frac{85}{2 \cdot 12} + \frac{35}{24}$

$145 = 165$

$120 = \frac{415}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

Step 2.3.6.8.1.1.2.2

Multiply $2$ by $12$ .

$a = - \frac{85}{24} + \frac{35}{24}$

$145 = 165$

$120 = \frac{415}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

$a = - \frac{85}{24} + \frac{35}{24}$

$145 = 165$

$120 = \frac{415}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

$a = - \frac{85}{24} + \frac{35}{24}$

$145 = 165$

$120 = \frac{415}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

Step 2.3.6.8.1.2

Simplify terms.

Tap for more steps...

Step 2.3.6.8.1.2.1

Combine the numerators over the common denominator.

$a = \frac{- 85 + 35}{24}$

$145 = 165$

$120 = \frac{415}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

Step 2.3.6.8.1.2.2

Add $- 85$ and $35$ .

$a = \frac{- 50}{24}$

$145 = 165$

$120 = \frac{415}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

Step 2.3.6.8.1.2.3

Cancel the common factor of $- 50$ and $24$ .

Tap for more steps...

Step 2.3.6.8.1.2.3.1

Factor $2$ out of $- 50$ .

$a = \frac{2 (- 25)}{24}$

$145 = 165$

$120 = \frac{415}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

Step 2.3.6.8.1.2.3.2

Cancel the common factors.

Tap for more steps...

Step 2.3.6.8.1.2.3.2.1

Factor $2$ out of $24$ .

$a = \frac{2 \cdot - 25}{2 \cdot 12}$

$145 = 165$

$120 = \frac{415}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

Step 2.3.6.8.1.2.3.2.2

Cancel the common factor.

$a = \frac{2 \cdot - 25}{2 \cdot 12}$

$145 = 165$

$120 = \frac{415}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

Step 2.3.6.8.1.2.3.2.3

Rewrite the expression.

$a = \frac{- 25}{12}$

$145 = 165$

$120 = \frac{415}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

$a = \frac{- 25}{12}$

$145 = 165$

$120 = \frac{415}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

$a = \frac{- 25}{12}$

$145 = 165$

$120 = \frac{415}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

Step 2.3.6.8.1.2.4

Move the negative in front of the fraction.

$a = - \frac{25}{12}$

$145 = 165$

$120 = \frac{415}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

$a = - \frac{25}{12}$

$145 = 165$

$120 = \frac{415}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

$a = - \frac{25}{12}$

$145 = 165$

$120 = \frac{415}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

$a = - \frac{25}{12}$

$145 = 165$

$120 = \frac{415}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

$a = - \frac{25}{12}$

$145 = 165$

$120 = \frac{415}{3}$

$c = - \frac{125}{3}$

$b = \frac{85}{2}$

Step 2.3.7

Since $145 = 165$ is not true, there is no solution.

No solution

Step 2.4

Calculate the value of $y$ using each $x$ value in the table and compare this value to the given $y$ value in the table.

Tap for more steps...

Step 2.4.1

Calculate the value of $y$ such that $y = a x^{2} + b$ when $a = 0$ , $b = 0$ , $c = 0$ , and $x = 2$ .

Tap for more steps...

Step 2.4.1.1

Simplify each term.

Tap for more steps...

Step 2.4.1.1.1

Raise $2$ to the power of $2$ .

$y = 0 \cdot 4 + (0) \cdot (2) + 0$

Step 2.4.1.1.2

Multiply $0$ by $4$ .

$y = 0 + (0) \cdot (2) + 0$

Step 2.4.1.1.3

Multiply $0$ by $2$ .

$y = 0 + 0 + 0$

Step 2.4.1.2

Simplify by adding numbers.

Tap for more steps...

Step 2.4.1.2.1

Add $0$ and $0$ .

$y = 0 + 0$

Step 2.4.1.2.2

Add $0$ and $0$ .

$y = 0$

Step 2.4.2

If the table has a quadratic function rule, $y = y$ for the corresponding $x$ value, $x = 2$ . This check does not pass, since $y = 0$ and $y = 35$ . The function rule can't be quadratic.

$0 \neq 35$

Step 2.4.3

Since $y \neq y$ for the corresponding $x$ values, the function is not quadratic.

The function is not quadratic

Step 3

Check if the function rule is cubic.

Tap for more steps...

Step 3.1

To find if the table follows a function rule, check whether the function rule could follow the form $y = a x^{3} + b x^{2} + c x + d$ .

$y = a x^{3} + b x^{2} + c x + d$

Step 3.2

Build a set of $4$ equations from the table such that $y = a x^{3} + b x^{2} + c x + d$ .

Step 3.3

Calculate the values of $a$ , $b$ , $c$ , and $d$ .

Tap for more steps...

Step 3.3.1

Solve for $d$ in $35 = a \cdot 2^{3} + b \cdot 2^{2} + c (2) + d$ .

Tap for more steps...

Step 3.3.1.1

Rewrite the equation as $a \cdot 2^{3} + b \cdot 2^{2} + c (2) + d = 35$ .

$a \cdot 2^{3} + b \cdot 2^{2} + c (2) + d = 35$

$95 = a \cdot 4^{3} + b \cdot 2^{2} + c (2) + d$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.1.2

Simplify each term.

Tap for more steps...

Step 3.3.1.2.1

Raise $2$ to the power of $3$ .

$a \cdot 8 + b \cdot 2^{2} + c (2) + d = 35$

$95 = a \cdot 4^{3} + b \cdot 2^{2} + c (2) + d$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.1.2.2

Move $8$ to the left of $a$ .

$8 \cdot a + b \cdot 2^{2} + c (2) + d = 35$

$95 = a \cdot 4^{3} + b \cdot 2^{2} + c (2) + d$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.1.2.3

Raise $2$ to the power of $2$ .

$8 a + b \cdot 4 + c (2) + d = 35$

$95 = a \cdot 4^{3} + b \cdot 2^{2} + c (2) + d$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.1.2.4

Move $4$ to the left of $b$ .

$8 a + 4 \cdot b + c (2) + d = 35$

$95 = a \cdot 4^{3} + b \cdot 2^{2} + c (2) + d$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.1.2.5

Move $2$ to the left of $c$ .

$8 a + 4 b + 2 c + d = 35$

$95 = a \cdot 4^{3} + b \cdot 2^{2} + c (2) + d$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

$8 a + 4 b + 2 c + d = 35$

$95 = a \cdot 4^{3} + b \cdot 2^{2} + c (2) + d$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.1.3

Move all terms not containing $d$ to the right side of the equation.

Tap for more steps...

Step 3.3.1.3.1

Subtract $8 a$ from both sides of the equation.

$4 b + 2 c + d = 35 - 8 a$

$95 = a \cdot 4^{3} + b \cdot 2^{2} + c (2) + d$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.1.3.2

Subtract $4 b$ from both sides of the equation.

$2 c + d = 35 - 8 a - 4 b$

$95 = a \cdot 4^{3} + b \cdot 2^{2} + c (2) + d$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.1.3.3

Subtract $2 c$ from both sides of the equation.

$d = 35 - 8 a - 4 b - 2 c$

$95 = a \cdot 4^{3} + b \cdot 2^{2} + c (2) + d$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

$d = 35 - 8 a - 4 b - 2 c$

$95 = a \cdot 4^{3} + b \cdot 2^{2} + c (2) + d$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

$d = 35 - 8 a - 4 b - 2 c$

$95 = a \cdot 4^{3} + b \cdot 2^{2} + c (2) + d$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2

Replace all occurrences of $d$ with $35 - 8 a - 4 b - 2 c$ in each equation.

Tap for more steps...

Step 3.3.2.1

Replace all occurrences of $d$ in $95 = a \cdot 4^{3} + b \cdot 2^{2} + c (2) + d$ with $35 - 8 a - 4 b - 2 c$ .

$95 = a \cdot 4^{3} + b \cdot 2^{2} + c (2) + 35 - 8 a - 4 b - 2 c$

$d = 35 - 8 a - 4 b - 2 c$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.2

Simplify $95 = a \cdot 4^{3} + b \cdot 2^{2} + c (2) + 35 - 8 a - 4 b - 2 c$ .

Tap for more steps...

Step 3.3.2.2.1

Simplify the left side.

Tap for more steps...

Step 3.3.2.2.1.1

Remove parentheses.

$95 = a \cdot 4^{3} + b \cdot 2^{2} + c (2) + 35 - 8 a - 4 b - 2 c$

$d = 35 - 8 a - 4 b - 2 c$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

$95 = a \cdot 4^{3} + b \cdot 2^{2} + c (2) + 35 - 8 a - 4 b - 2 c$

$d = 35 - 8 a - 4 b - 2 c$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.2.2

Simplify the right side.

Tap for more steps...

Step 3.3.2.2.2.1

Simplify $a \cdot 4^{3} + b \cdot 2^{2} + c (2) + 35 - 8 a - 4 b - 2 c$ .

Tap for more steps...

Step 3.3.2.2.2.1.1

Combine the opposite terms in $a \cdot 4^{3} + b \cdot 2^{2} + c (2) + 35 - 8 a - 4 b - 2 c$ .

Tap for more steps...

Step 3.3.2.2.2.1.1.1

Reorder the factors in the terms $c (2)$ and $- 2 c$ .

$95 = a \cdot 4^{3} + b \cdot 2^{2} + 2 c + 35 - 8 a - 4 b - 2 c$

$d = 35 - 8 a - 4 b - 2 c$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.2.2.1.1.2

Subtract $2 c$ from $2 c$ .

$95 = a \cdot 4^{3} + b \cdot 2^{2} + 35 - 8 a - 4 b + 0$

$d = 35 - 8 a - 4 b - 2 c$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.2.2.1.1.3

Add $a \cdot 4^{3} + b \cdot 2^{2} + 35 - 8 a - 4 b$ and $0$ .

$95 = a \cdot 4^{3} + b \cdot 2^{2} + 35 - 8 a - 4 b$

$d = 35 - 8 a - 4 b - 2 c$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

$95 = a \cdot 4^{3} + b \cdot 2^{2} + 35 - 8 a - 4 b$

$d = 35 - 8 a - 4 b - 2 c$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.2.2.1.2

Simplify each term.

Tap for more steps...

Step 3.3.2.2.2.1.2.1

Raise $4$ to the power of $3$ .

$95 = a \cdot 64 + b \cdot 2^{2} + 35 - 8 a - 4 b$

$d = 35 - 8 a - 4 b - 2 c$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.2.2.1.2.2

Move $64$ to the left of $a$ .

$95 = 64 \cdot a + b \cdot 2^{2} + 35 - 8 a - 4 b$

$d = 35 - 8 a - 4 b - 2 c$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.2.2.1.2.3

Raise $2$ to the power of $2$ .

$95 = 64 a + b \cdot 4 + 35 - 8 a - 4 b$

$d = 35 - 8 a - 4 b - 2 c$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.2.2.1.2.4

Move $4$ to the left of $b$ .

$95 = 64 a + 4 b + 35 - 8 a - 4 b$

$d = 35 - 8 a - 4 b - 2 c$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

$95 = 64 a + 4 b + 35 - 8 a - 4 b$

$d = 35 - 8 a - 4 b - 2 c$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.2.2.1.3

Simplify by adding terms.

Tap for more steps...

Step 3.3.2.2.2.1.3.1

Combine the opposite terms in $64 a + 4 b + 35 - 8 a - 4 b$ .

Tap for more steps...

Step 3.3.2.2.2.1.3.1.1

Subtract $4 b$ from $4 b$ .

$95 = 64 a + 35 - 8 a + 0$

$d = 35 - 8 a - 4 b - 2 c$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.2.2.1.3.1.2

Add $64 a + 35 - 8 a$ and $0$ .

$95 = 64 a + 35 - 8 a$

$d = 35 - 8 a - 4 b - 2 c$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

$95 = 64 a + 35 - 8 a$

$d = 35 - 8 a - 4 b - 2 c$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.2.2.1.3.2

Subtract $8 a$ from $64 a$ .

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.3

Replace all occurrences of $d$ in $120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + d$ with $35 - 8 a - 4 b - 2 c$ .

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + 35 - 8 a - 4 b - 2 c$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.4

Simplify $120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + 35 - 8 a - 4 b - 2 c$ .

Tap for more steps...

Step 3.3.2.4.1

Simplify the left side.

Tap for more steps...

Step 3.3.2.4.1.1

Remove parentheses.

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + 35 - 8 a - 4 b - 2 c$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + c (2) + 35 - 8 a - 4 b - 2 c$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.4.2

Simplify the right side.

Tap for more steps...

Step 3.3.2.4.2.1

Simplify $a \cdot 6^{3} + b \cdot 2^{2} + c (2) + 35 - 8 a - 4 b - 2 c$ .

Tap for more steps...

Step 3.3.2.4.2.1.1

Combine the opposite terms in $a \cdot 6^{3} + b \cdot 2^{2} + c (2) + 35 - 8 a - 4 b - 2 c$ .

Tap for more steps...

Step 3.3.2.4.2.1.1.1

Reorder the factors in the terms $c (2)$ and $- 2 c$ .

$120 = a \cdot 6^{3} + b \cdot 2^{2} + 2 c + 35 - 8 a - 4 b - 2 c$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.4.2.1.1.2

Subtract $2 c$ from $2 c$ .

$120 = a \cdot 6^{3} + b \cdot 2^{2} + 35 - 8 a - 4 b + 0$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.4.2.1.1.3

Add $a \cdot 6^{3} + b \cdot 2^{2} + 35 - 8 a - 4 b$ and $0$ .

$120 = a \cdot 6^{3} + b \cdot 2^{2} + 35 - 8 a - 4 b$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

$120 = a \cdot 6^{3} + b \cdot 2^{2} + 35 - 8 a - 4 b$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.4.2.1.2

Simplify each term.

Tap for more steps...

Step 3.3.2.4.2.1.2.1

Raise $6$ to the power of $3$ .

$120 = a \cdot 216 + b \cdot 2^{2} + 35 - 8 a - 4 b$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.4.2.1.2.2

Move $216$ to the left of $a$ .

$120 = 216 \cdot a + b \cdot 2^{2} + 35 - 8 a - 4 b$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.4.2.1.2.3

Raise $2$ to the power of $2$ .

$120 = 216 a + b \cdot 4 + 35 - 8 a - 4 b$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.4.2.1.2.4

Move $4$ to the left of $b$ .

$120 = 216 a + 4 b + 35 - 8 a - 4 b$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

$120 = 216 a + 4 b + 35 - 8 a - 4 b$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.4.2.1.3

Simplify by adding terms.

Tap for more steps...

Step 3.3.2.4.2.1.3.1

Combine the opposite terms in $216 a + 4 b + 35 - 8 a - 4 b$ .

Tap for more steps...

Step 3.3.2.4.2.1.3.1.1

Subtract $4 b$ from $4 b$ .

$120 = 216 a + 35 - 8 a + 0$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.4.2.1.3.1.2

Add $216 a + 35 - 8 a$ and $0$ .

$120 = 216 a + 35 - 8 a$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

$120 = 216 a + 35 - 8 a$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.4.2.1.3.2

Subtract $8 a$ from $216 a$ .

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.5

Replace all occurrences of $d$ in $145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + d$ with $35 - 8 a - 4 b - 2 c$ .

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + 35 - 8 a - 4 b - 2 c$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.6

Simplify $145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + 35 - 8 a - 4 b - 2 c$ .

Tap for more steps...

Step 3.3.2.6.1

Simplify the left side.

Tap for more steps...

Step 3.3.2.6.1.1

Remove parentheses.

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + 35 - 8 a - 4 b - 2 c$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + c (2) + 35 - 8 a - 4 b - 2 c$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.6.2

Simplify the right side.

Tap for more steps...

Step 3.3.2.6.2.1

Simplify $a \cdot 8^{3} + b \cdot 2^{2} + c (2) + 35 - 8 a - 4 b - 2 c$ .

Tap for more steps...

Step 3.3.2.6.2.1.1

Combine the opposite terms in $a \cdot 8^{3} + b \cdot 2^{2} + c (2) + 35 - 8 a - 4 b - 2 c$ .

Tap for more steps...

Step 3.3.2.6.2.1.1.1

Reorder the factors in the terms $c (2)$ and $- 2 c$ .

$145 = a \cdot 8^{3} + b \cdot 2^{2} + 2 c + 35 - 8 a - 4 b - 2 c$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.6.2.1.1.2

Subtract $2 c$ from $2 c$ .

$145 = a \cdot 8^{3} + b \cdot 2^{2} + 35 - 8 a - 4 b + 0$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.6.2.1.1.3

Add $a \cdot 8^{3} + b \cdot 2^{2} + 35 - 8 a - 4 b$ and $0$ .

$145 = a \cdot 8^{3} + b \cdot 2^{2} + 35 - 8 a - 4 b$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

$145 = a \cdot 8^{3} + b \cdot 2^{2} + 35 - 8 a - 4 b$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.6.2.1.2

Simplify each term.

Tap for more steps...

Step 3.3.2.6.2.1.2.1

Raise $8$ to the power of $3$ .

$145 = a \cdot 512 + b \cdot 2^{2} + 35 - 8 a - 4 b$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.6.2.1.2.2

Move $512$ to the left of $a$ .

$145 = 512 \cdot a + b \cdot 2^{2} + 35 - 8 a - 4 b$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.6.2.1.2.3

Raise $2$ to the power of $2$ .

$145 = 512 a + b \cdot 4 + 35 - 8 a - 4 b$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.6.2.1.2.4

Move $4$ to the left of $b$ .

$145 = 512 a + 4 b + 35 - 8 a - 4 b$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

$145 = 512 a + 4 b + 35 - 8 a - 4 b$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.6.2.1.3

Simplify by adding terms.

Tap for more steps...

Step 3.3.2.6.2.1.3.1

Combine the opposite terms in $512 a + 4 b + 35 - 8 a - 4 b$ .

Tap for more steps...

Step 3.3.2.6.2.1.3.1.1

Subtract $4 b$ from $4 b$ .

$145 = 512 a + 35 - 8 a + 0$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.6.2.1.3.1.2

Add $512 a + 35 - 8 a$ and $0$ .

$145 = 512 a + 35 - 8 a$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

$145 = 512 a + 35 - 8 a$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.6.2.1.3.2

Subtract $8 a$ from $512 a$ .

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$

Step 3.3.2.7

Replace all occurrences of $d$ in $175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + d$ with $35 - 8 a - 4 b - 2 c$ .

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + 35 - 8 a - 4 b - 2 c$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.2.8

Simplify $175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + 35 - 8 a - 4 b - 2 c$ .

Tap for more steps...

Step 3.3.2.8.1

Simplify the left side.

Tap for more steps...

Step 3.3.2.8.1.1

Remove parentheses.

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + 35 - 8 a - 4 b - 2 c$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + c (2) + 35 - 8 a - 4 b - 2 c$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.2.8.2

Simplify the right side.

Tap for more steps...

Step 3.3.2.8.2.1

Simplify $a \cdot 10^{3} + b \cdot 2^{2} + c (2) + 35 - 8 a - 4 b - 2 c$ .

Tap for more steps...

Step 3.3.2.8.2.1.1

Combine the opposite terms in $a \cdot 10^{3} + b \cdot 2^{2} + c (2) + 35 - 8 a - 4 b - 2 c$ .

Tap for more steps...

Step 3.3.2.8.2.1.1.1

Reorder the factors in the terms $c (2)$ and $- 2 c$ .

$175 = a \cdot 10^{3} + b \cdot 2^{2} + 2 c + 35 - 8 a - 4 b - 2 c$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.2.8.2.1.1.2

Subtract $2 c$ from $2 c$ .

$175 = a \cdot 10^{3} + b \cdot 2^{2} + 35 - 8 a - 4 b + 0$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.2.8.2.1.1.3

Add $a \cdot 10^{3} + b \cdot 2^{2} + 35 - 8 a - 4 b$ and $0$ .

$175 = a \cdot 10^{3} + b \cdot 2^{2} + 35 - 8 a - 4 b$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$175 = a \cdot 10^{3} + b \cdot 2^{2} + 35 - 8 a - 4 b$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.2.8.2.1.2

Simplify each term.

Tap for more steps...

Step 3.3.2.8.2.1.2.1

Raise $10$ to the power of $3$ .

$175 = a \cdot 1000 + b \cdot 2^{2} + 35 - 8 a - 4 b$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.2.8.2.1.2.2

Move $1000$ to the left of $a$ .

$175 = 1000 \cdot a + b \cdot 2^{2} + 35 - 8 a - 4 b$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.2.8.2.1.2.3

Raise $2$ to the power of $2$ .

$175 = 1000 a + b \cdot 4 + 35 - 8 a - 4 b$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.2.8.2.1.2.4

Move $4$ to the left of $b$ .

$175 = 1000 a + 4 b + 35 - 8 a - 4 b$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$175 = 1000 a + 4 b + 35 - 8 a - 4 b$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.2.8.2.1.3

Simplify by adding terms.

Tap for more steps...

Step 3.3.2.8.2.1.3.1

Combine the opposite terms in $1000 a + 4 b + 35 - 8 a - 4 b$ .

Tap for more steps...

Step 3.3.2.8.2.1.3.1.1

Subtract $4 b$ from $4 b$ .

$175 = 1000 a + 35 - 8 a + 0$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.2.8.2.1.3.1.2

Add $1000 a + 35 - 8 a$ and $0$ .

$175 = 1000 a + 35 - 8 a$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$175 = 1000 a + 35 - 8 a$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.2.8.2.1.3.2

Subtract $8 a$ from $1000 a$ .

$175 = 992 a + 35$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$175 = 992 a + 35$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$175 = 992 a + 35$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$175 = 992 a + 35$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$175 = 992 a + 35$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$175 = 992 a + 35$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.3

Solve for $a$ in $175 = 992 a + 35$ .

Tap for more steps...

Step 3.3.3.1

Rewrite the equation as $992 a + 35 = 175$ .

$992 a + 35 = 175$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.3.2

Move all terms not containing $a$ to the right side of the equation.

Tap for more steps...

Step 3.3.3.2.1

Subtract $35$ from both sides of the equation.

$992 a = 175 - 35$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.3.2.2

Subtract $35$ from $175$ .

$992 a = 140$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$992 a = 140$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.3.3

Divide each term in $992 a = 140$ by $992$ and simplify.

Tap for more steps...

Step 3.3.3.3.1

Divide each term in $992 a = 140$ by $992$ .

$\frac{992 a}{992} = \frac{140}{992}$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.3.3.2

Simplify the left side.

Tap for more steps...

Step 3.3.3.3.2.1

Cancel the common factor of $992$ .

Tap for more steps...

Step 3.3.3.3.2.1.1

Cancel the common factor.

$\frac{992 a}{992} = \frac{140}{992}$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.3.3.2.1.2

Divide $a$ by $1$ .

$a = \frac{140}{992}$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$a = \frac{140}{992}$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$a = \frac{140}{992}$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.3.3.3

Simplify the right side.

Tap for more steps...

Step 3.3.3.3.3.1

Cancel the common factor of $140$ and $992$ .

Tap for more steps...

Step 3.3.3.3.3.1.1

Factor $4$ out of $140$ .

$a = \frac{4 (35)}{992}$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.3.3.3.1.2

Cancel the common factors.

Tap for more steps...

Step 3.3.3.3.3.1.2.1

Factor $4$ out of $992$ .

$a = \frac{4 \cdot 35}{4 \cdot 248}$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.3.3.3.1.2.2

Cancel the common factor.

$a = \frac{4 \cdot 35}{4 \cdot 248}$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.3.3.3.1.2.3

Rewrite the expression.

$a = \frac{35}{248}$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$a = \frac{35}{248}$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$a = \frac{35}{248}$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$a = \frac{35}{248}$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$a = \frac{35}{248}$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$a = \frac{35}{248}$

$145 = 504 a + 35$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4

Replace all occurrences of $a$ with $\frac{35}{248}$ in each equation.

Tap for more steps...

Step 3.3.4.1

Replace all occurrences of $a$ in $145 = 504 a + 35$ with $\frac{35}{248}$ .

$145 = 504 (\frac{35}{248}) + 35$

$a = \frac{35}{248}$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.2

Simplify the right side.

Tap for more steps...

Step 3.3.4.2.1

Simplify $504 (\frac{35}{248}) + 35$ .

Tap for more steps...

Step 3.3.4.2.1.1

Simplify each term.

Tap for more steps...

Step 3.3.4.2.1.1.1

Cancel the common factor of $8$ .

Tap for more steps...

Step 3.3.4.2.1.1.1.1

Factor $8$ out of $504$ .

$145 = 8 (63) (\frac{35}{248}) + 35$

$a = \frac{35}{248}$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.2.1.1.1.2

Factor $8$ out of $248$ .

$145 = 8 \cdot (63 (\frac{35}{8 \cdot 31})) + 35$

$a = \frac{35}{248}$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.2.1.1.1.3

Cancel the common factor.

$145 = 8 \cdot (63 (\frac{35}{8 \cdot 31})) + 35$

$a = \frac{35}{248}$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.2.1.1.1.4

Rewrite the expression.

$145 = 63 (\frac{35}{31}) + 35$

$a = \frac{35}{248}$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$145 = 63 (\frac{35}{31}) + 35$

$a = \frac{35}{248}$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.2.1.1.2

Combine $63$ and $\frac{35}{31}$ .

$145 = \frac{63 \cdot 35}{31} + 35$

$a = \frac{35}{248}$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.2.1.1.3

Multiply $63$ by $35$ .

$145 = \frac{2205}{31} + 35$

$a = \frac{35}{248}$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$145 = \frac{2205}{31} + 35$

$a = \frac{35}{248}$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.2.1.2

To write $35$ as a fraction with a common denominator, multiply by $\frac{31}{31}$ .

$145 = \frac{2205}{31} + 35 \cdot \frac{31}{31}$

$a = \frac{35}{248}$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.2.1.3

Combine $35$ and $\frac{31}{31}$ .

$145 = \frac{2205}{31} + \frac{35 \cdot 31}{31}$

$a = \frac{35}{248}$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.2.1.4

Combine the numerators over the common denominator.

$145 = \frac{2205 + 35 \cdot 31}{31}$

$a = \frac{35}{248}$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.2.1.5

Simplify the numerator.

Tap for more steps...

Step 3.3.4.2.1.5.1

Multiply $35$ by $31$ .

$145 = \frac{2205 + 1085}{31}$

$a = \frac{35}{248}$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.2.1.5.2

Add $2205$ and $1085$ .

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$120 = 208 a + 35$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.3

Replace all occurrences of $a$ in $120 = 208 a + 35$ with $\frac{35}{248}$ .

$120 = 208 (\frac{35}{248}) + 35$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.4

Simplify the right side.

Tap for more steps...

Step 3.3.4.4.1

Simplify $208 (\frac{35}{248}) + 35$ .

Tap for more steps...

Step 3.3.4.4.1.1

Simplify each term.

Tap for more steps...

Step 3.3.4.4.1.1.1

Cancel the common factor of $8$ .

Tap for more steps...

Step 3.3.4.4.1.1.1.1

Factor $8$ out of $208$ .

$120 = 8 (26) (\frac{35}{248}) + 35$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.4.1.1.1.2

Factor $8$ out of $248$ .

$120 = 8 \cdot (26 (\frac{35}{8 \cdot 31})) + 35$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.4.1.1.1.3

Cancel the common factor.

$120 = 8 \cdot (26 (\frac{35}{8 \cdot 31})) + 35$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.4.1.1.1.4

Rewrite the expression.

$120 = 26 (\frac{35}{31}) + 35$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$120 = 26 (\frac{35}{31}) + 35$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.4.1.1.2

Combine $26$ and $\frac{35}{31}$ .

$120 = \frac{26 \cdot 35}{31} + 35$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.4.1.1.3

Multiply $26$ by $35$ .

$120 = \frac{910}{31} + 35$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$120 = \frac{910}{31} + 35$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.4.1.2

To write $35$ as a fraction with a common denominator, multiply by $\frac{31}{31}$ .

$120 = \frac{910}{31} + 35 \cdot \frac{31}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.4.1.3

Combine $35$ and $\frac{31}{31}$ .

$120 = \frac{910}{31} + \frac{35 \cdot 31}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.4.1.4

Combine the numerators over the common denominator.

$120 = \frac{910 + 35 \cdot 31}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.4.1.5

Simplify the numerator.

Tap for more steps...

Step 3.3.4.4.1.5.1

Multiply $35$ by $31$ .

$120 = \frac{910 + 1085}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.4.1.5.2

Add $910$ and $1085$ .

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$95 = 56 a + 35$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.5

Replace all occurrences of $a$ in $95 = 56 a + 35$ with $\frac{35}{248}$ .

$95 = 56 (\frac{35}{248}) + 35$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.6

Simplify the right side.

Tap for more steps...

Step 3.3.4.6.1

Simplify $56 (\frac{35}{248}) + 35$ .

Tap for more steps...

Step 3.3.4.6.1.1

Simplify each term.

Tap for more steps...

Step 3.3.4.6.1.1.1

Cancel the common factor of $8$ .

Tap for more steps...

Step 3.3.4.6.1.1.1.1

Factor $8$ out of $56$ .

$95 = 8 (7) (\frac{35}{248}) + 35$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.6.1.1.1.2

Factor $8$ out of $248$ .

$95 = 8 \cdot (7 (\frac{35}{8 \cdot 31})) + 35$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.6.1.1.1.3

Cancel the common factor.

$95 = 8 \cdot (7 (\frac{35}{8 \cdot 31})) + 35$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.6.1.1.1.4

Rewrite the expression.

$95 = 7 (\frac{35}{31}) + 35$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$d = 35 - 8 a - 4 b - 2 c$

$95 = 7 (\frac{35}{31}) + 35$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.6.1.1.2

Combine $7$ and $\frac{35}{31}$ .

$95 = \frac{7 \cdot 35}{31} + 35$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.6.1.1.3

Multiply $7$ by $35$ .

$95 = \frac{245}{31} + 35$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$d = 35 - 8 a - 4 b - 2 c$

$95 = \frac{245}{31} + 35$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.6.1.2

To write $35$ as a fraction with a common denominator, multiply by $\frac{31}{31}$ .

$95 = \frac{245}{31} + 35 \cdot \frac{31}{31}$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.6.1.3

Combine $35$ and $\frac{31}{31}$ .

$95 = \frac{245}{31} + \frac{35 \cdot 31}{31}$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.6.1.4

Combine the numerators over the common denominator.

$95 = \frac{245 + 35 \cdot 31}{31}$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.6.1.5

Simplify the numerator.

Tap for more steps...

Step 3.3.4.6.1.5.1

Multiply $35$ by $31$ .

$95 = \frac{245 + 1085}{31}$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.6.1.5.2

Add $245$ and $1085$ .

$95 = \frac{1330}{31}$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$d = 35 - 8 a - 4 b - 2 c$

$95 = \frac{1330}{31}$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$d = 35 - 8 a - 4 b - 2 c$

$95 = \frac{1330}{31}$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$d = 35 - 8 a - 4 b - 2 c$

$95 = \frac{1330}{31}$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$d = 35 - 8 a - 4 b - 2 c$

Step 3.3.4.7

Replace all occurrences of $a$ in $d = 35 - 8 a - 4 b - 2 c$ with $\frac{35}{248}$ .

$d = 35 - 8 (\frac{35}{248}) - 4 b - 2 c$

$95 = \frac{1330}{31}$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

Step 3.3.4.8

Simplify the right side.

Tap for more steps...

Step 3.3.4.8.1

Simplify $35 - 8 (\frac{35}{248}) - 4 b - 2 c$ .

Tap for more steps...

Step 3.3.4.8.1.1

Simplify each term.

Tap for more steps...

Step 3.3.4.8.1.1.1

Cancel the common factor of $8$ .

Tap for more steps...

Step 3.3.4.8.1.1.1.1

Factor $8$ out of $- 8$ .

$d = 35 + 8 (- 1) (\frac{35}{248}) - 4 b - 2 c$

$95 = \frac{1330}{31}$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

Step 3.3.4.8.1.1.1.2

Factor $8$ out of $248$ .

$d = 35 + 8 \cdot (- 1 \frac{35}{8 \cdot 31}) - 4 b - 2 c$

$95 = \frac{1330}{31}$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

Step 3.3.4.8.1.1.1.3

Cancel the common factor.

$d = 35 + 8 \cdot (- 1 \frac{35}{8 \cdot 31}) - 4 b - 2 c$

$95 = \frac{1330}{31}$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

Step 3.3.4.8.1.1.1.4

Rewrite the expression.

$d = 35 - 1 (\frac{35}{31}) - 4 b - 2 c$

$95 = \frac{1330}{31}$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$d = 35 - 1 (\frac{35}{31}) - 4 b - 2 c$

$95 = \frac{1330}{31}$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

Step 3.3.4.8.1.1.2

Rewrite $- 1 (\frac{35}{31})$ as $- (\frac{35}{31})$ .

$d = 35 - \frac{35}{31} - 4 b - 2 c$

$95 = \frac{1330}{31}$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$d = 35 - \frac{35}{31} - 4 b - 2 c$

$95 = \frac{1330}{31}$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

Step 3.3.4.8.1.2

To write $35$ as a fraction with a common denominator, multiply by $\frac{31}{31}$ .

$d = 35 \cdot \frac{31}{31} - \frac{35}{31} - 4 b - 2 c$

$95 = \frac{1330}{31}$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

Step 3.3.4.8.1.3

Combine $35$ and $\frac{31}{31}$ .

$d = \frac{35 \cdot 31}{31} - \frac{35}{31} - 4 b - 2 c$

$95 = \frac{1330}{31}$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

Step 3.3.4.8.1.4

Combine the numerators over the common denominator.

$d = \frac{35 \cdot 31 - 35}{31} - 4 b - 2 c$

$95 = \frac{1330}{31}$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

Step 3.3.4.8.1.5

Simplify the numerator.

Tap for more steps...

Step 3.3.4.8.1.5.1

Multiply $35$ by $31$ .

$d = \frac{1085 - 35}{31} - 4 b - 2 c$

$95 = \frac{1330}{31}$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

Step 3.3.4.8.1.5.2

Subtract $35$ from $1085$ .

$d = \frac{1050}{31} - 4 b - 2 c$

$95 = \frac{1330}{31}$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$d = \frac{1050}{31} - 4 b - 2 c$

$95 = \frac{1330}{31}$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$d = \frac{1050}{31} - 4 b - 2 c$

$95 = \frac{1330}{31}$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$d = \frac{1050}{31} - 4 b - 2 c$

$95 = \frac{1330}{31}$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

$d = \frac{1050}{31} - 4 b - 2 c$

$95 = \frac{1330}{31}$

$120 = \frac{1995}{31}$

$145 = \frac{3290}{31}$

$a = \frac{35}{248}$

Step 3.3.5

Since $95 = \frac{1330}{31}$ is not true, there is no solution.

No solution

Step 3.4

Calculate the value of $y$ using each $x$ value in the table and compare this value to the given $y$ value in the table.

Tap for more steps...

Step 3.4.1

Calculate the value of $y$ such that $y = a x^{3} + b$ when $a = 0$ , $b = 0$ , $c = 0$ , $d = 0$ , and $x = 2$ .

Tap for more steps...

Step 3.4.1.1

Simplify each term.

Tap for more steps...

Step 3.4.1.1.1

Raise $2$ to the power of $3$ .

$y = 0 \cdot 8 + (0) \cdot (2^{2}) + (0) \cdot ((2) \cdot 0)$

Step 3.4.1.1.2

Multiply $0$ by $8$ .

$y = 0 + (0) \cdot (2^{2}) + (0) \cdot ((2) \cdot 0)$

Step 3.4.1.1.3

Raise $2$ to the power of $2$ .

$y = 0 + 0 \cdot 4 + (0) \cdot ((2) \cdot 0)$

Step 3.4.1.1.4

Multiply $0$ by $4$ .

$y = 0 + 0 + (0) \cdot ((2) \cdot 0)$

Step 3.4.1.1.5

Multiply $(0) ((2) \cdot 0)$ .

Tap for more steps...

Step 3.4.1.1.5.1

Multiply $2$ by $0$ .

$y = 0 + 0 + 0 \cdot 0$

Step 3.4.1.1.5.2

Multiply $0$ by $0$ .

$y = 0 + 0 + 0$

Step 3.4.1.2

Simplify by adding numbers.

Tap for more steps...

Step 3.4.1.2.1

Add $0$ and $0$ .

$y = 0 + 0$

Step 3.4.1.2.2

Add $0$ and $0$ .

$y = 0$

Step 3.4.2

If the table has a cubic function rule, $y = y$ for the corresponding $x$ value, $x = 2$ . This check does not pass, since $y = 0$ and $y = 35$ . The function rule can't be cubic.

$0 \neq 35$

Step 3.4.3

Since $y \neq y$ for the corresponding $x$ values, the function is not cubic.

The function is not cubic

Step 4

There are no values for $a$ , $b$ , $c$ , and $d$ in the equations $y = a x + b$ , $y = a x^{2} + b x + c$ , and $y = a x^{3} + b x^{2} + c x + d$ that work for every pair of $x$ and $y$ .

The table does not have a function rule that is linear, quadratic, or cubic.