Solve by Graphing 4x+2y=-2 x-3y=24

$4 x + 2 y = - 2$ $x - 3 y = 24$

Step 1

Subtract $4 x$ from both sides of the equation.

$2 y = - 2 - 4 x$

$x - 3 y = 24$

Step 2

Divide each term in $2 y = - 2 - 4 x$ by $2$ and simplify.

Divide each term in $2 y = - 2 - 4 x$ by $2$ .

$\frac{2 y}{2} = \frac{- 2}{2} + \frac{- 4 x}{2}$

$x - 3 y = 24$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{- 2}{2} + \frac{- 4 x}{2}$

$x - 3 y = 24$

Divide $y$ by $1$ .

$y = \frac{- 2}{2} + \frac{- 4 x}{2}$

$x - 3 y = 24$

$y = \frac{- 2}{2} + \frac{- 4 x}{2}$

$x - 3 y = 24$

$y = \frac{- 2}{2} + \frac{- 4 x}{2}$

$x - 3 y = 24$

Simplify the right side.

Simplify each term.

Divide $- 2$ by $2$ .

$y = - 1 + \frac{- 4 x}{2}$

$x - 3 y = 24$

Cancel the common factor of $- 4$ and $2$ .

Factor $2$ out of $- 4 x$ .

$y = - 1 + \frac{2 (- 2 x)}{2}$

$x - 3 y = 24$

Cancel the common factors.

Factor $2$ out of $2$ .

$y = - 1 + \frac{2 (- 2 x)}{2 (1)}$

$x - 3 y = 24$

Cancel the common factor.

$y = - 1 + \frac{2 (- 2 x)}{2 \cdot 1}$

$x - 3 y = 24$

Rewrite the expression.

$y = - 1 + \frac{- 2 x}{1}$

$x - 3 y = 24$

Divide $- 2 x$ by $1$ .

$y = - 1 - 2 x$

$x - 3 y = 24$

$y = - 1 - 2 x$

$x - 3 y = 24$

$y = - 1 - 2 x$

$x - 3 y = 24$

$y = - 1 - 2 x$

$x - 3 y = 24$

$y = - 1 - 2 x$

$x - 3 y = 24$

$y = - 1 - 2 x$

$x - 3 y = 24$

Step 3

Subtract $x$ from both sides of the equation.

$- 3 y = 24 - x$

$y = - 1 - 2 x$

Step 4

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

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

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

$y = - 1 - 2 x$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

$y = - 1 - 2 x$

Divide $y$ by $1$ .

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

$y = - 1 - 2 x$

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

$y = - 1 - 2 x$

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

$y = - 1 - 2 x$

Simplify the right side.

Simplify each term.

Divide $24$ by $- 3$ .

$y = - 8 + \frac{- x}{- 3}$

$y = - 1 - 2 x$

Dividing two negative values results in a positive value.

$y = - 8 + \frac{x}{3}$

$y = - 1 - 2 x$

$y = - 8 + \frac{x}{3}$

$y = - 1 - 2 x$

$y = - 8 + \frac{x}{3}$

$y = - 1 - 2 x$

$y = - 8 + \frac{x}{3}$

$y = - 1 - 2 x$

Step 5

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

$(3, - 7)$

Step 6

Solve by Graphing 4x+2y=-2 x-3y=24

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