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

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

Step 1

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

$x = 4 + 4 y$

$- x + 4 y = - 4$

Step 2

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

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

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

$x = 4 + 4 y$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

$- 1 \cdot 4 - (4 y) + 4 y = - 4$

$x = 4 + 4 y$

Multiply $- 1$ by $4$ .

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

$x = 4 + 4 y$

Multiply $4$ by $- 1$ .

$- 4 - 4 y + 4 y = - 4$

$x = 4 + 4 y$

$- 4 - 4 y + 4 y = - 4$

$x = 4 + 4 y$

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

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

$- 4 + 0 = - 4$

$x = 4 + 4 y$

Add $- 4$ and $0$ .

$- 4 = - 4$

$x = 4 + 4 y$

$- 4 = - 4$

$x = 4 + 4 y$

$- 4 = - 4$

$x = 4 + 4 y$

$- 4 = - 4$

$x = 4 + 4 y$

$- 4 = - 4$

$x = 4 + 4 y$

Step 3

Remove any equations from the system that are always true.

$x = 4 + 4 y$

Step 4