Solve the System of Equations y=3x-2 and y=-x-6

$y = 3 x - 2$ and $y = - x - 6$

Eliminate the equal sides of each equation and combine.

$3 x - 2 = - x - 6$

Solve $3 x - 2 = - x - 6$ for $x$ .

Move all terms containing $x$ to the left side of the equation.

Add $x$ to both sides of the equation.

$3 x - 2 + x = - 6$

Add $3 x$ and $x$ .

$4 x - 2 = - 6$

Move all terms not containing $x$ to the right side of the equation.

Add $2$ to both sides of the equation.

$4 x = - 6 + 2$

Add $- 6$ and $2$ .

$4 x = - 4$

Divide each term in $4 x = - 4$ by $4$ and simplify.

Divide each term in $4 x = - 4$ by $4$ .

$\frac{4 x}{4} = \frac{- 4}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 4}{4}$

Divide $x$ by $1$ .

$x = \frac{- 4}{4}$

Simplify the right side.

Divide $- 4$ by $4$ .

$x = - 1$

Evaluate $y$ when $x = - 1$ .

Substitute $- 1$ for $x$ .

$y = - (- 1) - 6$

Simplify $- (- 1) - 6$ .

Multiply $- 1$ by $- 1$ .

$y = 1 - 6$

Subtract $6$ from $1$ .

$y = - 5$

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(- 1, - 5)$

The result can be shown in multiple forms.

Point Form:

$(- 1, - 5)$

Equation Form:

$x = - 1, y = - 5$