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.

$- 1 \cdot 9 - (3 y) + 3 y = - 9$

$x = 9 + 3 y$

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