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

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

Step 1

Subtract $4 y$ from 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 $- 4 + 4 y - 4 y$ .

Subtract $4 y$ from $4 y$ .

$- 4 + 0 = - 4$

$x = 4 - 4 y$

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