Solve the System of Equations -x+5y=-5 x-5y=5

$- x + 5 y = - 5$ $x - 5 y = 5$

Add $5 y$ to both sides of the equation.

$x = 5 + 5 y$

$- x + 5 y = - 5$

Replace all occurrences of $x$ with $5 + 5 y$ in each equation.

Replace all occurrences of $x$ in $- x + 5 y = - 5$ with $5 + 5 y$ .

$- (5 + 5 y) + 5 y = - 5$

$x = 5 + 5 y$

Simplify the left side.

Simplify $- (5 + 5 y) + 5 y$ .

Simplify each term.

Apply the distributive property.

$- 1 \cdot 5 - (5 y) + 5 y = - 5$

$x = 5 + 5 y$

Multiply $- 1$ by $5$ .

$- 5 - (5 y) + 5 y = - 5$

$x = 5 + 5 y$

Multiply $5$ by $- 1$ .

$- 5 - 5 y + 5 y = - 5$

$x = 5 + 5 y$

$- 5 - 5 y + 5 y = - 5$

$x = 5 + 5 y$

Combine the opposite terms in $- 5 - 5 y + 5 y$ .

Add $- 5 y$ and $5 y$ .

$- 5 + 0 = - 5$

$x = 5 + 5 y$

Add $- 5$ and $0$ .

$- 5 = - 5$

$x = 5 + 5 y$

$- 5 = - 5$

$x = 5 + 5 y$

$- 5 = - 5$

$x = 5 + 5 y$

$- 5 = - 5$

$x = 5 + 5 y$

$- 5 = - 5$

$x = 5 + 5 y$

Remove any equations from the system that are always true.

$x = 5 + 5 y$

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