Solve xy^2=8*y^2=

$$x y ^ { 2 } = 8 \cdot y ^ { 2 } =$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=8\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$y^{2}x=8y^{2}$$

Divide both sides by y^{2}.

$$\frac{y^{2}x}{y^{2}}=\frac{8y^{2}}{y^{2}}$$

Dividing by y^{2} undoes the multiplication by y^{2}.

$$x=\frac{8y^{2}}{y^{2}}$$

Divide 8y^{2} by y^{2}.

$$x=8$$

Solve for y (complex solution)

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=8\end{matrix}\right.$$

Steps by Finding Square Root

Subtract 8y^{2} from both sides.

$$xy^{2}-8y^{2}=0$$

Combine all terms containing y.

$$\left(x-8\right)y^{2}=0$$

Dividing by -8+x undoes the multiplication by -8+x.

$$y^{2}=\frac{0}{x-8}$$

Divide 0 by -8+x.

$$y^{2}=0$$

Take the square root of both sides of the equation.

$$y=0 y=0$$

The equation is now solved. Solutions are the same.

$$y=0$$

Steps Using the Quadratic Formula

Subtract 8y^{2} from both sides.

$$xy^{2}-8y^{2}=0$$

Combine all terms containing y.

$$\left(x-8\right)y^{2}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -8+x for a, 0 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}}}{2\left(x-8\right)}$$

Take the square root of 0^{2}.

$$y=\frac{0±0}{2\left(x-8\right)}$$

Multiply 2 times -8+x.

$$y=\frac{0}{2x-16}$$

Divide 0 by -16+2x.

$$y=0$$

Solve for x

$$\left\{\begin{matrix}\\x=8\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$y^{2}x=8y^{2}$$

Divide both sides by y^{2}.

$$\frac{y^{2}x}{y^{2}}=\frac{8y^{2}}{y^{2}}$$

Dividing by y^{2} undoes the multiplication by y^{2}.

$$x=\frac{8y^{2}}{y^{2}}$$

Divide 8y^{2} by y^{2}.

$$x=8$$

Solve for y

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=8\end{matrix}\right.$$