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

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

Step 1

Subtract $2 y$ from 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.

$- 1 \cdot 2 - (- 2 y) - 2 y = - 2$

$x = 2 - 2 y$

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 $- 2 + 2 y - 2 y$ .

Subtract $2 y$ from $2 y$ .

$- 2 + 0 = - 2$

$x = 2 - 2 y$

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