Solve by Substitution -x+2y=2 , x-2y=-2

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

Step 1

Add $2 y$ to both sides of the equation.

$x = - 2 + 2 y$

$- x + 2 y = 2$

Step 2

Replace all occurrences of $x$ with $- 2 + 2 y$ in each equation.

Replace all occurrences of $x$ in $- x + 2 y = 2$ with $- 2 + 2 y$ .

$- (- 2 + 2 y) + 2 y = 2$

$x = - 2 + 2 y$

Simplify the left side.

Simplify $- (- 2 + 2 y) + 2 y$ .

Simplify each term.

Apply the distributive property.

$2 - (2 y) + 2 y = 2$

$x = - 2 + 2 y$

Multiply $- 1$ by $- 2$ .

$2 - (2 y) + 2 y = 2$

$x = - 2 + 2 y$

Multiply $2$ by $- 1$ .

$2 - 2 y + 2 y = 2$

$x = - 2 + 2 y$

$2 - 2 y + 2 y = 2$

$x = - 2 + 2 y$

Combine the opposite terms in $2 - 2 y + 2 y$ .

Add $- 2 y$ and $2 y$ .

$2 + 0 = 2$

$x = - 2 + 2 y$

Add $2$ and $0$ .

$2 = 2$

$x = - 2 + 2 y$

$2 = 2$

$x = - 2 + 2 y$

$2 = 2$

$x = - 2 + 2 y$

$2 = 2$

$x = - 2 + 2 y$

$2 = 2$

$x = - 2 + 2 y$

Step 3

Remove any equations from the system that are always true.

$x = - 2 + 2 y$

Step 4