Solve for x y^2=x^2

$y^{2} = x^{2}$

Rewrite the equation as $x^{2} = y^{2}$ .

$x^{2} = y^{2}$

Since the exponents are equal, the bases of the exponents on both sides of the equation must be equal.

$| x | = | y |$

Solve for $x$ .

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$x = \pm | y |$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = | y |$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - | y |$

The complete solution is the result of both the positive and negative portions of the solution.

$x = | y |$

$x = - | y |$

$x = | y |$

$x = - | y |$

$x = | y |$

$x = - | y |$