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.

$- 1 \cdot 6 - (3 y) + 3 y = 6$

$x = 6 + 3 y$

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

Since $- 6 = 6$ is not true, there is no solution.

No solution

Step 4