Solve the System of Equations 3x-y=6 and -3x+y=-6

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

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

$y = - 6 + 3 x$

$3 x - y = 6$

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

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

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

$y = - 6 + 3 x$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

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

$y = - 6 + 3 x$

Multiply $- 1$ by $- 6$ .

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

$y = - 6 + 3 x$

Multiply $3$ by $- 1$ .

$3 x + 6 - 3 x = 6$

$y = - 6 + 3 x$

$3 x + 6 - 3 x = 6$

$y = - 6 + 3 x$

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

Subtract $3 x$ from $3 x$ .

$0 + 6 = 6$

$y = - 6 + 3 x$

Add $0$ and $6$ .

$6 = 6$

$y = - 6 + 3 x$

$6 = 6$

$y = - 6 + 3 x$

$6 = 6$

$y = - 6 + 3 x$

$6 = 6$

$y = - 6 + 3 x$

$6 = 6$

$y = - 6 + 3 x$

Remove any equations from the system that are always true.

$y = - 6 + 3 x$

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