Solve by Graphing 2x+y=13 3x+2y=-20

$2 x + y = 13$ $3 x + 2 y = - 20$

Step 1

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

$y = 13 - 2 x$

$3 x + 2 y = - 20$

Step 2

Subtract $3 x$ from both sides of the equation.

$2 y = - 20 - 3 x$

$y = 13 - 2 x$

Step 3

Divide each term in $2 y = - 20 - 3 x$ by $2$ and simplify.

Divide each term in $2 y = - 20 - 3 x$ by $2$ .

$\frac{2 y}{2} = \frac{- 20}{2} + \frac{- 3 x}{2}$

$y = 13 - 2 x$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{- 20}{2} + \frac{- 3 x}{2}$

$y = 13 - 2 x$

Divide $y$ by $1$ .

$y = \frac{- 20}{2} + \frac{- 3 x}{2}$

$y = 13 - 2 x$

$y = \frac{- 20}{2} + \frac{- 3 x}{2}$

$y = 13 - 2 x$

$y = \frac{- 20}{2} + \frac{- 3 x}{2}$

$y = 13 - 2 x$

Simplify the right side.

Simplify each term.

Divide $- 20$ by $2$ .

$y = - 10 + \frac{- 3 x}{2}$

$y = 13 - 2 x$

Move the negative in front of the fraction.

$y = - 10 - \frac{3 x}{2}$

$y = 13 - 2 x$

$y = - 10 - \frac{3 x}{2}$

$y = 13 - 2 x$

$y = - 10 - \frac{3 x}{2}$

$y = 13 - 2 x$

$y = - 10 - \frac{3 x}{2}$

$y = 13 - 2 x$

Step 4

Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution.

$(46, - 79)$

Step 5