Solve by Graphing x-2y=10 , x+2y=-2

$x - 2 y = 10$ , $x + 2 y = - 2$

Step 1

Subtract $x$ from both sides of the equation.

$- 2 y = 10 - x$

$x + 2 y = - 2$

Step 2

Divide each term in $- 2 y = 10 - x$ by $- 2$ and simplify.

Divide each term in $- 2 y = 10 - x$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{10}{- 2} + \frac{- x}{- 2}$

$x + 2 y = - 2$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{10}{- 2} + \frac{- x}{- 2}$

$x + 2 y = - 2$

Divide $y$ by $1$ .

$y = \frac{10}{- 2} + \frac{- x}{- 2}$

$x + 2 y = - 2$

$y = \frac{10}{- 2} + \frac{- x}{- 2}$

$x + 2 y = - 2$

$y = \frac{10}{- 2} + \frac{- x}{- 2}$

$x + 2 y = - 2$

Simplify the right side.

Simplify each term.

Divide $10$ by $- 2$ .

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

$x + 2 y = - 2$

Dividing two negative values results in a positive value.

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

$x + 2 y = - 2$

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

$x + 2 y = - 2$

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

$x + 2 y = - 2$

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

$x + 2 y = - 2$

Step 3

Subtract $x$ from both sides of the equation.

$2 y = - 2 - x$

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

Step 4

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

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

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

Divide $y$ by $1$ .

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

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

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

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

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

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

Simplify the right side.

Simplify each term.

Divide $- 2$ by $2$ .

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

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

Move the negative in front of the fraction.

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

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

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

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

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

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

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

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

Step 5

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

$(4, - 3)$

Step 6

Solve by Graphing x-2y=10 , x+2y=-2

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