Solve by Graphing 5x-2y=-8 3x-4y=12

$5 x - 2 y = - 8$ $3 x - 4 y = 12$

Step 1

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

$- 2 y = - 8 - 5 x$

$3 x - 4 y = 12$

Step 2

Divide each term in $- 2 y = - 8 - 5 x$ by $- 2$ and simplify.

Divide each term in $- 2 y = - 8 - 5 x$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 8}{- 2} + \frac{- 5 x}{- 2}$

$3 x - 4 y = 12$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 8}{- 2} + \frac{- 5 x}{- 2}$

$3 x - 4 y = 12$

Divide $y$ by $1$ .

$y = \frac{- 8}{- 2} + \frac{- 5 x}{- 2}$

$3 x - 4 y = 12$

$y = \frac{- 8}{- 2} + \frac{- 5 x}{- 2}$

$3 x - 4 y = 12$

$y = \frac{- 8}{- 2} + \frac{- 5 x}{- 2}$

$3 x - 4 y = 12$

Simplify the right side.

Simplify each term.

Divide $- 8$ by $- 2$ .

$y = 4 + \frac{- 5 x}{- 2}$

$3 x - 4 y = 12$

Dividing two negative values results in a positive value.

$y = 4 + \frac{5 x}{2}$

$3 x - 4 y = 12$

$y = 4 + \frac{5 x}{2}$

$3 x - 4 y = 12$

$y = 4 + \frac{5 x}{2}$

$3 x - 4 y = 12$

$y = 4 + \frac{5 x}{2}$

$3 x - 4 y = 12$

Step 3

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

$- 4 y = 12 - 3 x$

$y = 4 + \frac{5 x}{2}$

Step 4

Divide each term in $- 4 y = 12 - 3 x$ by $- 4$ and simplify.

Divide each term in $- 4 y = 12 - 3 x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{12}{- 4} + \frac{- 3 x}{- 4}$

$y = 4 + \frac{5 x}{2}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{12}{- 4} + \frac{- 3 x}{- 4}$

$y = 4 + \frac{5 x}{2}$

Divide $y$ by $1$ .

$y = \frac{12}{- 4} + \frac{- 3 x}{- 4}$

$y = 4 + \frac{5 x}{2}$

$y = \frac{12}{- 4} + \frac{- 3 x}{- 4}$

$y = 4 + \frac{5 x}{2}$

$y = \frac{12}{- 4} + \frac{- 3 x}{- 4}$

$y = 4 + \frac{5 x}{2}$

Simplify the right side.

Simplify each term.

Divide $12$ by $- 4$ .

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

$y = 4 + \frac{5 x}{2}$

Dividing two negative values results in a positive value.

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

$y = 4 + \frac{5 x}{2}$

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

$y = 4 + \frac{5 x}{2}$

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

$y = 4 + \frac{5 x}{2}$

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

$y = 4 + \frac{5 x}{2}$

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 5x-2y=-8 3x-4y=12

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