Solve by Graphing 6x+4y=-12 x-4y=-2

$6 x + 4 y = - 12$ $x - 4 y = - 2$

Step 1

Subtract $6 x$ from both sides of the equation.

$4 y = - 12 - 6 x$

$x - 4 y = - 2$

Step 2

Divide each term in $4 y = - 12 - 6 x$ by $4$ and simplify.

Divide each term in $4 y = - 12 - 6 x$ by $4$ .

$\frac{4 y}{4} = \frac{- 12}{4} + \frac{- 6 x}{4}$

$x - 4 y = - 2$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{- 12}{4} + \frac{- 6 x}{4}$

$x - 4 y = - 2$

Divide $y$ by $1$ .

$y = \frac{- 12}{4} + \frac{- 6 x}{4}$

$x - 4 y = - 2$

$y = \frac{- 12}{4} + \frac{- 6 x}{4}$

$x - 4 y = - 2$

$y = \frac{- 12}{4} + \frac{- 6 x}{4}$

$x - 4 y = - 2$

Simplify the right side.

Simplify each term.

Divide $- 12$ by $4$ .

$y = - 3 + \frac{- 6 x}{4}$

$x - 4 y = - 2$

Cancel the common factor of $- 6$ and $4$ .

Factor $2$ out of $- 6 x$ .

$y = - 3 + \frac{2 (- 3 x)}{4}$

$x - 4 y = - 2$

Cancel the common factors.

Factor $2$ out of $4$ .

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

$x - 4 y = - 2$

Cancel the common factor.

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

$x - 4 y = - 2$

Rewrite the expression.

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

$x - 4 y = - 2$

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

$x - 4 y = - 2$

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

$x - 4 y = - 2$

Move the negative in front of the fraction.

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

$x - 4 y = - 2$

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

$x - 4 y = - 2$

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

$x - 4 y = - 2$

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

$x - 4 y = - 2$

Step 3

Subtract $x$ from both sides of the equation.

$- 4 y = - 2 - x$

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

Step 4

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

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

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

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

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

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

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

Divide $y$ by $1$ .

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

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

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

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

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

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

Simplify the right side.

Simplify each term.

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

Factor $- 2$ out of $- 2$ .

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

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

Cancel the common factors.

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

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

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

Cancel the common factor.

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

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

Rewrite the expression.

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

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

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

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

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

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

Dividing two negative values results in a positive value.

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

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

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

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

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

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

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

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

Step 5

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

$(- 2, 0)$

Step 6

Solve by Graphing 6x+4y=-12 x-4y=-2

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