Finite Math Examples

$2 a + b = 7$ , $2 a + 1.5 b = 21$

Step 1

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

$b = 7 - 2 a$

$2 a + 1.5 b = 21$

Step 2

Replace all occurrences of $b$ with $7 - 2 a$ in each equation.

Tap for more steps...

Step 2.1

Replace all occurrences of $b$ in $2 a + 1.5 b = 21$ with $7 - 2 a$ .

$2 a + 1.5 (7 - 2 a) = 21$

$b = 7 - 2 a$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify $2 a + 1.5 (7 - 2 a)$ .

Tap for more steps...

Step 2.2.1.1

Simplify each term.

Tap for more steps...

Step 2.2.1.1.1

Apply the distributive property.

$2 a + 1.5 \cdot 7 + 1.5 (- 2 a) = 21$

$b = 7 - 2 a$

Step 2.2.1.1.2

Multiply $1.5$ by $7$ .

$2 a + 10.5 + 1.5 (- 2 a) = 21$

$b = 7 - 2 a$

Step 2.2.1.1.3

Multiply $- 2$ by $1.5$ .

$2 a + 10.5 - 3 a = 21$

$b = 7 - 2 a$

$2 a + 10.5 - 3 a = 21$

$b = 7 - 2 a$

Step 2.2.1.2

Subtract $3 a$ from $2 a$ .

$- 1 a + 10.5 = 21$

$b = 7 - 2 a$

$- 1 a + 10.5 = 21$

$b = 7 - 2 a$

$- 1 a + 10.5 = 21$

$b = 7 - 2 a$

$- 1 a + 10.5 = 21$

$b = 7 - 2 a$

Step 3

Solve for $a$ in $- 1 a + 10.5 = 21$ .

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

Subtract $10.5$ from both sides of the equation.

$- 1 a = 21 - 10.5$

$b = 7 - 2 a$

Step 3.1.2

Subtract $10.5$ from $21$ .

$- 1 a = 10.5$

$b = 7 - 2 a$

$- 1 a = 10.5$

$b = 7 - 2 a$

Step 3.2

Divide each term in $- 1 a = 10.5$ by $- 1$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in $- 1 a = 10.5$ by $- 1$ .

$\frac{- 1 a}{- 1} = \frac{10.5}{- 1}$

$b = 7 - 2 a$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $- 1$ .

Tap for more steps...

Step 3.2.2.1.1

Rewrite $- 1$ as $- 1 (1)$ .

$\frac{- 1 \cdot 1 a}{- 1} = \frac{10.5}{- 1}$

$b = 7 - 2 a$

Step 3.2.2.1.2

Factor $1$ out of $- 1 (1) a$ .

$\frac{1 (- 1 \cdot (1 a))}{- 1} = \frac{10.5}{- 1}$

$b = 7 - 2 a$

Step 3.2.2.1.3

Move the negative one from the denominator of $\frac{- 1 \cdot 1 a}{- 1}$ .

$- 1 \cdot (- 1 \cdot (1 a)) = \frac{10.5}{- 1}$

$b = 7 - 2 a$

$- 1 \cdot (- 1 \cdot (1 a)) = \frac{10.5}{- 1}$

$b = 7 - 2 a$

Step 3.2.2.2

Simplify the expression.

Tap for more steps...

Step 3.2.2.2.1

Rewrite $- 1 \cdot (- 1 \cdot 1 a)$ as $- (- 1 \cdot 1 a)$ .

$- (- 1 \cdot (1 a)) = \frac{10.5}{- 1}$

$b = 7 - 2 a$

Step 3.2.2.2.2

Multiply $- 1$ by $1$ .

$- (- 1 a) = \frac{10.5}{- 1}$

$b = 7 - 2 a$

Step 3.2.2.2.3

Rewrite $- 1 a$ as $- a$ .

$a = \frac{10.5}{- 1}$

$b = 7 - 2 a$

$a = \frac{10.5}{- 1}$

$b = 7 - 2 a$

Step 3.2.2.3

Multiply $- - a$ .

Tap for more steps...

Step 3.2.2.3.1

Multiply $- 1$ by $- 1$ .

$1 a = \frac{10.5}{- 1}$

$b = 7 - 2 a$

Step 3.2.2.3.2

Multiply $a$ by $1$ .

$a = \frac{10.5}{- 1}$

$b = 7 - 2 a$

$a = \frac{10.5}{- 1}$

$b = 7 - 2 a$

$a = \frac{10.5}{- 1}$

$b = 7 - 2 a$

Step 3.2.3

Simplify the right side.

Tap for more steps...

Step 3.2.3.1

Divide $10.5$ by $- 1$ .

$a = - 10.5$

$b = 7 - 2 a$

$a = - 10.5$

$b = 7 - 2 a$

$a = - 10.5$

$b = 7 - 2 a$

$a = - 10.5$

$b = 7 - 2 a$

Step 4

Replace all occurrences of $a$ with $- 10.5$ in each equation.

Tap for more steps...

Step 4.1

Replace all occurrences of $a$ in $b = 7 - 2 a$ with $- 10.5$ .

$b = 7 - 2 \cdot - 10.5$

$a = - 10.5$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Simplify $7 - 2 \cdot - 10.5$ .

Tap for more steps...

Step 4.2.1.1

Multiply $- 2$ by $- 10.5$ .

$b = 7 + 21$

$a = - 10.5$

Step 4.2.1.2

Add $7$ and $21$ .

$b = 28$

$a = - 10.5$

$b = 28$

$a = - 10.5$

$b = 28$

$a = - 10.5$

$b = 28$

$a = - 10.5$

Step 5

List all of the solutions.

$b = 28, a = - 10.5$