Solve by Graphing x-2y=8 , 2x+4y=12

$x - 2 y = 8$ , $2 x + 4 y = 12$

Step 1

Subtract $x$ from both sides of the equation.

$- 2 y = 8 - x$

$2 x + 4 y = 12$

Step 2

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

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

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

$2 x + 4 y = 12$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

$2 x + 4 y = 12$

Divide $y$ by $1$ .

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

$2 x + 4 y = 12$

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

$2 x + 4 y = 12$

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

$2 x + 4 y = 12$

Simplify the right side.

Simplify each term.

Divide $8$ by $- 2$ .

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

$2 x + 4 y = 12$

Dividing two negative values results in a positive value.

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

$2 x + 4 y = 12$

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

$2 x + 4 y = 12$

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

$2 x + 4 y = 12$

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

$2 x + 4 y = 12$

Step 3

Subtract $2 x$ from both sides of the equation.

$4 y = 12 - 2 x$

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

Step 4

Divide each term in $4 y = 12 - 2 x$ by $4$ and simplify.

Divide each term in $4 y = 12 - 2 x$ by $4$ .

$\frac{4 y}{4} = \frac{12}{4} + \frac{- 2 x}{4}$

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{12}{4} + \frac{- 2 x}{4}$

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

Divide $y$ by $1$ .

$y = \frac{12}{4} + \frac{- 2 x}{4}$

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

$y = \frac{12}{4} + \frac{- 2 x}{4}$

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

$y = \frac{12}{4} + \frac{- 2 x}{4}$

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

Simplify the right side.

Simplify each term.

Divide $12$ by $4$ .

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

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

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

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

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

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

Cancel the common factors.

Factor $2$ out of $4$ .

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

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

Cancel the common factor.

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

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

Rewrite the expression.

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

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

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

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

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

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

Move the negative in front of the fraction.

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

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

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

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

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

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

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

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

Step 5

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

$(7, - \frac{1}{2})$

Step 6

Solve by Graphing x-2y=8 , 2x+4y=12

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