Solve by Substitution -x+3y=6 , x-3y=-6

$- x + 3 y = 6$ , $x - 3 y = - 6$

Step 1

Add $3 y$ to both sides of the equation.

$x = - 6 + 3 y$

$- x + 3 y = 6$

Step 2

Replace all occurrences of $x$ with $- 6 + 3 y$ in each equation.

Replace all occurrences of $x$ in $- x + 3 y = 6$ with $- 6 + 3 y$ .

$- (- 6 + 3 y) + 3 y = 6$

$x = - 6 + 3 y$

Simplify the left side.

Simplify $- (- 6 + 3 y) + 3 y$ .

Simplify each term.

Apply the distributive property.

$6 - (3 y) + 3 y = 6$

$x = - 6 + 3 y$

Multiply $- 1$ by $- 6$ .

$6 - (3 y) + 3 y = 6$

$x = - 6 + 3 y$

Multiply $3$ by $- 1$ .

$6 - 3 y + 3 y = 6$

$x = - 6 + 3 y$

$6 - 3 y + 3 y = 6$

$x = - 6 + 3 y$

Combine the opposite terms in $6 - 3 y + 3 y$ .

Add $- 3 y$ and $3 y$ .

$6 + 0 = 6$

$x = - 6 + 3 y$

Add $6$ and $0$ .

$6 = 6$

$x = - 6 + 3 y$

$6 = 6$

$x = - 6 + 3 y$

$6 = 6$

$x = - 6 + 3 y$

$6 = 6$

$x = - 6 + 3 y$

$6 = 6$

$x = - 6 + 3 y$

Step 3

Remove any equations from the system that are always true.

$x = - 6 + 3 y$

Step 4