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

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

Step 1

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

$- 2 y = 6 - 3 x$

$y = - 3 x - 3$

Step 2

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

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

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

$y = - 3 x - 3$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

$y = - 3 x - 3$

Divide $y$ by $1$ .

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

$y = - 3 x - 3$

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

$y = - 3 x - 3$

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

$y = - 3 x - 3$

Simplify the right side.

Simplify each term.

Divide $6$ by $- 2$ .

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

$y = - 3 x - 3$

Dividing two negative values results in a positive value.

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

$y = - 3 x - 3$

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

$y = - 3 x - 3$

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

$y = - 3 x - 3$

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

$y = - 3 x - 3$

Step 3

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

$(0, - 3)$

Step 4