Solve for y x^2-y^2=0

$x^{2} - y^{2} = 0$

Step 1

Subtract $x^{2}$ from both sides of the equation.

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

Step 2

Divide each term in $- y^{2} = - x^{2}$ by $- 1$ and simplify.

Divide each term in $- y^{2} = - x^{2}$ by $- 1$ .

$\frac{- y^{2}}{- 1} = \frac{- x^{2}}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y^{2}}{1} = \frac{- x^{2}}{- 1}$

Divide $y^{2}$ by $1$ .

$y^{2} = \frac{- x^{2}}{- 1}$

Simplify the right side.

Dividing two negative values results in a positive value.

$y^{2} = \frac{x^{2}}{1}$

Divide $x^{2}$ by $1$ .

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

Step 3

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

$| y | = | x |$

Step 4

Solve for $y$ .

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

$y = \pm | x |$

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.

$y = | x |$

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

$y = - | x |$

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

$y = | x |$

$y = - | x |$

$y = | x |$

$y = - | x |$

$y = | x |$

$y = - | x |$