Solve by Graphing 3x-2y=-24 , -3x-y=6

$3 x - 2 y = - 24$ , $- 3 x - y = 6$

Step 1

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

$- 2 y = - 24 - 3 x$

$- 3 x - y = 6$

Step 2

Divide each term in $- 2 y = - 24 - 3 x$ by $- 2$ and simplify.

Divide each term in $- 2 y = - 24 - 3 x$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 24}{- 2} + \frac{- 3 x}{- 2}$

$- 3 x - y = 6$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 24}{- 2} + \frac{- 3 x}{- 2}$

$- 3 x - y = 6$

Divide $y$ by $1$ .

$y = \frac{- 24}{- 2} + \frac{- 3 x}{- 2}$

$- 3 x - y = 6$

$y = \frac{- 24}{- 2} + \frac{- 3 x}{- 2}$

$- 3 x - y = 6$

$y = \frac{- 24}{- 2} + \frac{- 3 x}{- 2}$

$- 3 x - y = 6$

Simplify the right side.

Simplify each term.

Divide $- 24$ by $- 2$ .

$y = 12 + \frac{- 3 x}{- 2}$

$- 3 x - y = 6$

Dividing two negative values results in a positive value.

$y = 12 + \frac{3 x}{2}$

$- 3 x - y = 6$

$y = 12 + \frac{3 x}{2}$

$- 3 x - y = 6$

$y = 12 + \frac{3 x}{2}$

$- 3 x - y = 6$

$y = 12 + \frac{3 x}{2}$

$- 3 x - y = 6$

Step 3

Add $3 x$ to both sides of the equation.

$- y = 6 + 3 x$

$y = 12 + \frac{3 x}{2}$

Step 4

Divide each term in $- y = 6 + 3 x$ by $- 1$ and simplify.

Divide each term in $- y = 6 + 3 x$ by $- 1$ .

$\frac{- y}{- 1} = \frac{6}{- 1} + \frac{3 x}{- 1}$

$y = 12 + \frac{3 x}{2}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{6}{- 1} + \frac{3 x}{- 1}$

$y = 12 + \frac{3 x}{2}$

Divide $y$ by $1$ .

$y = \frac{6}{- 1} + \frac{3 x}{- 1}$

$y = 12 + \frac{3 x}{2}$

$y = \frac{6}{- 1} + \frac{3 x}{- 1}$

$y = 12 + \frac{3 x}{2}$

Simplify the right side.

Simplify each term.

Divide $6$ by $- 1$ .

$y = - 6 + \frac{3 x}{- 1}$

$y = 12 + \frac{3 x}{2}$

Move the negative one from the denominator of $\frac{3 x}{- 1}$ .

$y = - 6 - 1 \cdot (3 x)$

$y = 12 + \frac{3 x}{2}$

Rewrite $- 1 \cdot (3 x)$ as $- (3 x)$ .

$y = - 6 - (3 x)$

$y = 12 + \frac{3 x}{2}$

Multiply $3$ by $- 1$ .

$y = - 6 - 3 x$

$y = 12 + \frac{3 x}{2}$

$y = - 6 - 3 x$

$y = 12 + \frac{3 x}{2}$

$y = - 6 - 3 x$

$y = 12 + \frac{3 x}{2}$

$y = - 6 - 3 x$

$y = 12 + \frac{3 x}{2}$

Step 5

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

$(- 4, 6)$

Step 6

Solve by Graphing 3x-2y=-24 , -3x-y=6

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