Solve by Graphing 2x-3y=6 , 5x+y=-2

$2 x - 3 y = 6$ , $5 x + y = - 2$

Step 1

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

$- 3 y = 6 - 2 x$

$5 x + y = - 2$

Step 2

Divide each term in $- 3 y = 6 - 2 x$ by $- 3$ and simplify.

Divide each term in $- 3 y = 6 - 2 x$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{6}{- 3} + \frac{- 2 x}{- 3}$

$5 x + y = - 2$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{6}{- 3} + \frac{- 2 x}{- 3}$

$5 x + y = - 2$

Divide $y$ by $1$ .

$y = \frac{6}{- 3} + \frac{- 2 x}{- 3}$

$5 x + y = - 2$

$y = \frac{6}{- 3} + \frac{- 2 x}{- 3}$

$5 x + y = - 2$

$y = \frac{6}{- 3} + \frac{- 2 x}{- 3}$

$5 x + y = - 2$

Simplify the right side.

Simplify each term.

Divide $6$ by $- 3$ .

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

$5 x + y = - 2$

Dividing two negative values results in a positive value.

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

$5 x + y = - 2$

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

$5 x + y = - 2$

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

$5 x + y = - 2$

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

$5 x + y = - 2$

Step 3

Subtract $5 x$ from both sides of the equation.

$y = - 2 - 5 x$

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

Step 4

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

$(0, - 2)$

Step 5