Solve by Substitution -x+4y=8 , x-4y=-8

$- x + 4 y = 8$ , $x - 4 y = - 8$

Step 1

Add $4 y$ to both sides of the equation.

$x = - 8 + 4 y$

$- x + 4 y = 8$

Step 2

Replace all occurrences of $x$ with $- 8 + 4 y$ in each equation.

Replace all occurrences of $x$ in $- x + 4 y = 8$ with $- 8 + 4 y$ .

$- (- 8 + 4 y) + 4 y = 8$

$x = - 8 + 4 y$

Simplify the left side.

Simplify $- (- 8 + 4 y) + 4 y$ .

Simplify each term.

Apply the distributive property.

$8 - (4 y) + 4 y = 8$

$x = - 8 + 4 y$

Multiply $- 1$ by $- 8$ .

$8 - (4 y) + 4 y = 8$

$x = - 8 + 4 y$

Multiply $4$ by $- 1$ .

$8 - 4 y + 4 y = 8$

$x = - 8 + 4 y$

$8 - 4 y + 4 y = 8$

$x = - 8 + 4 y$

Combine the opposite terms in $8 - 4 y + 4 y$ .

Add $- 4 y$ and $4 y$ .

$8 + 0 = 8$

$x = - 8 + 4 y$

Add $8$ and $0$ .

$8 = 8$

$x = - 8 + 4 y$

$8 = 8$

$x = - 8 + 4 y$

$8 = 8$

$x = - 8 + 4 y$

$8 = 8$

$x = - 8 + 4 y$

$8 = 8$

$x = - 8 + 4 y$

Step 3

Remove any equations from the system that are always true.

$x = - 8 + 4 y$

Step 4