Solve yx^2-y=xy

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

Solve for y (complex solution)

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=\frac{\sqrt{5}+1}{2}\text{ or }x=\frac{1-\sqrt{5}}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract xy from both sides.

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

Combine all terms containing y.

$$\left(x^{2}-1-x\right)y=0$$

The equation is in standard form.

$$\left(x^{2}-x-1\right)y=0$$

Divide 0 by x^{2}-1-x.

$$y=0$$

Solve for y

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=\frac{\sqrt{5}+1}{2}\text{ or }x=\frac{1-\sqrt{5}}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract xy from both sides.

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

Combine all terms containing y.

$$\left(x^{2}-1-x\right)y=0$$

The equation is in standard form.

$$\left(x^{2}-x-1\right)y=0$$

Divide 0 by x^{2}-1-x.

$$y=0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=\frac{\sqrt{5}+1}{2}\approx 1.618033989\text{; }x=\frac{1-\sqrt{5}}{2}\approx -0.618033989\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&y=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}\\x=\frac{\sqrt{5}+1}{2}\approx 1.618033989\text{; }x=\frac{1-\sqrt{5}}{2}\approx -0.618033989\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=0\end{matrix}\right.$$