Solve the System of Equations y=x y=-x

$y = x$ $y = - x$

Eliminate the equal sides of each equation and combine.

$x = - x$

Solve $x = - x$ for $x$ .

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

Add $x$ to both sides of the equation.

$x + x = 0$

Add $x$ and $x$ .

$2 x = 0$

Divide each term in $2 x = 0$ by $2$ and simplify.

Divide each term in $2 x = 0$ by $2$ .

$\frac{2 x}{2} = \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{0}{2}$

Divide $x$ by $1$ .

$x = \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

$x = 0$

Evaluate $y$ when $x = 0$ .

Substitute $0$ for $x$ .

$y = - (0)$

Multiply $- 1$ by $0$ .

$y = 0$

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

$(0, 0)$

The result can be shown in multiple forms.

Point Form:

$(0, 0)$

Equation Form:

$x = 0, y = 0$