Finite Math Examples

$y = - x + 40$ , $y = - 2 x + 70$ , $y = - \frac{1}{3} x + 30$

Step 1

Eliminate the equal sides of each equation and combine.

$- x + 40 = - 2 x + 70$

Step 2

Solve $- x + 40 = - 2 x + 70$ for $x$ .

Tap for more steps...

Step 2.1

Move all terms containing $x$ to the left side of the equation.

Tap for more steps...

Step 2.1.1

Add $2 x$ to both sides of the equation.

$- x + 40 + 2 x = 70 + y = - 2 x + 70$

$y = - \frac{1}{3} x + 30$

Step 2.1.2

Add $- x$ and $2 x$ .

$x + 40 = 70 + y = - 2 x + 70$

$y = - \frac{1}{3} x + 30$

$x + 40 = 70 + y = - 2 x + 70$

$y = - \frac{1}{3} x + 30$

Step 2.2

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

Tap for more steps...

Step 2.2.1

Subtract $40$ from both sides of the equation.

$x = 70 - 40 + y = - 2 x + 70$

$y = - \frac{1}{3} x + 30$

Step 2.2.2

Subtract $40$ from $70$ .

$x = 30 + y = - 2 x + 70$

$y = - \frac{1}{3} x + 30$

$x = 30 + y = - 2 x + 70$

$y = - \frac{1}{3} x + 30$

$x = 30 + y = - 2 x + 70$

$y = - \frac{1}{3} x + 30$

Step 3

Evaluate $y$ when $x = 30$ .

Tap for more steps...

Step 3.1

Substitute $30$ for $x$ .

$y = - 2 \cdot 30 + 70 y = - \frac{1}{3} \cdot 30 + 30$

Step 3.2

Substitute $30$ for $x$ in $y = - 2 \cdot 30 + 70$ and solve for $y$ .

Tap for more steps...

Step 3.2.1

Remove parentheses.

$y = - 2 \cdot 30 + 70$

Step 3.2.2

Simplify $- 2 \cdot 30 + 70$ .

Tap for more steps...

Step 3.2.2.1

Multiply $- 2$ by $30$ .

$y = - 60 + 70$

Step 3.2.2.2

Add $- 60$ and $70$ .

$y = 10$

Step 4

Substitute $30$ for $x$ in $y = - \frac{1}{3} \cdot 30 + 30$ and solve for $y$ .

Tap for more steps...

Step 4.1

Remove parentheses.

$y = - \frac{1}{3} \cdot 30 + 30$

Step 4.2

Simplify $- \frac{1}{3} \cdot 30 + 30$ .

Tap for more steps...

Step 4.2.1

Simplify each term.

Tap for more steps...

Step 4.2.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.2.1.1.1

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$y = \frac{- 1}{3} \cdot 30 + 30$

Step 4.2.1.1.2

Factor $3$ out of $30$ .

$y = \frac{- 1}{3} \cdot (3 (10)) + 30$

Step 4.2.1.1.3

Cancel the common factor.

$y = \frac{- 1}{3} \cdot (3 \cdot 10) + 30$

Step 4.2.1.1.4

Rewrite the expression.

$y = - 1 \cdot 10 + 30$

Step 4.2.1.2

Multiply $- 1$ by $10$ .

$y = - 10 + 30$

Step 4.2.2

Add $- 10$ and $30$ .

$y = 20$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(30, 20)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(30, 20)$

Equation Form:

$x = 30, y = 20$

Step 7