Solve by Substitution -x+3y=9 , x-3y=-9

$- x + 3 y = 9$ , $x - 3 y = - 9$

Step 1

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

$x = - 9 + 3 y$

$- x + 3 y = 9$

Step 2

Replace all occurrences of $x$ with $- 9 + 3 y$ in each equation.

Replace all occurrences of $x$ in $- x + 3 y = 9$ with $- 9 + 3 y$ .

$- (- 9 + 3 y) + 3 y = 9$

$x = - 9 + 3 y$

Simplify the left side.

Simplify $- (- 9 + 3 y) + 3 y$ .

Simplify each term.

Apply the distributive property.

$9 - (3 y) + 3 y = 9$

$x = - 9 + 3 y$

Multiply $- 1$ by $- 9$ .

$9 - (3 y) + 3 y = 9$

$x = - 9 + 3 y$

Multiply $3$ by $- 1$ .

$9 - 3 y + 3 y = 9$

$x = - 9 + 3 y$

$9 - 3 y + 3 y = 9$

$x = - 9 + 3 y$

Combine the opposite terms in $9 - 3 y + 3 y$ .

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

$9 + 0 = 9$

$x = - 9 + 3 y$

Add $9$ and $0$ .

$9 = 9$

$x = - 9 + 3 y$

$9 = 9$

$x = - 9 + 3 y$

$9 = 9$

$x = - 9 + 3 y$

$9 = 9$

$x = - 9 + 3 y$

$9 = 9$

$x = - 9 + 3 y$

Step 3

Remove any equations from the system that are always true.

$x = - 9 + 3 y$

Step 4