Solve the System of Equations -x+2y=8 x-2y=-8

$- x + 2 y = 8$ $x - 2 y = - 8$

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

$x = - 8 + 2 y$

$- x + 2 y = 8$

Replace all occurrences of $x$ with $- 8 + 2 y$ in each equation.

Replace all occurrences of $x$ in $- x + 2 y = 8$ with $- 8 + 2 y$ .

$- (- 8 + 2 y) + 2 y = 8$

$x = - 8 + 2 y$

Simplify the left side.

Simplify $- (- 8 + 2 y) + 2 y$ .

Simplify each term.

Apply the distributive property.

$8 - (2 y) + 2 y = 8$

$x = - 8 + 2 y$

Multiply $- 1$ by $- 8$ .

$8 - (2 y) + 2 y = 8$

$x = - 8 + 2 y$

Multiply $2$ by $- 1$ .

$8 - 2 y + 2 y = 8$

$x = - 8 + 2 y$

$8 - 2 y + 2 y = 8$

$x = - 8 + 2 y$

Combine the opposite terms in $8 - 2 y + 2 y$ .

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

$8 + 0 = 8$

$x = - 8 + 2 y$

Add $8$ and $0$ .

$8 = 8$

$x = - 8 + 2 y$

$8 = 8$

$x = - 8 + 2 y$

$8 = 8$

$x = - 8 + 2 y$

$8 = 8$

$x = - 8 + 2 y$

$8 = 8$

$x = - 8 + 2 y$

Remove any equations from the system that are always true.

$x = - 8 + 2 y$

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