Solve the System of Equations y=-x-1 y=x+3

$y = - x - 1$ $y = x + 3$

Eliminate the equal sides of each equation and combine.

$- x - 1 = x + 3$

Solve $- x - 1 = x + 3$ for $x$ .

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

Subtract $x$ from both sides of the equation.

$- x - 1 - x = 3$

Subtract $x$ from $- x$ .

$- 2 x - 1 = 3$

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

Add $1$ to both sides of the equation.

$- 2 x = 3 + 1$

Add $3$ and $1$ .

$- 2 x = 4$

Divide each term in $- 2 x = 4$ by $- 2$ and simplify.

Divide each term in $- 2 x = 4$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{4}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{4}{- 2}$

Divide $x$ by $1$ .

$x = \frac{4}{- 2}$

Simplify the right side.

Divide $4$ by $- 2$ .

$x = - 2$

Evaluate $y$ when $x = - 2$ .

Substitute $- 2$ for $x$ .

$y = (- 2) + 3$

Substitute $- 2$ for $x$ in $y = (- 2) + 3$ and solve for $y$ .

Remove parentheses.

$y = - 2 + 3$

Remove parentheses.

$y = (- 2) + 3$

Add $- 2$ and $3$ .

$y = 1$

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

$(- 2, 1)$

The result can be shown in multiple forms.

Point Form:

$(- 2, 1)$

Equation Form:

$x = - 2, y = 1$