Solve xy_{1}=x^2

$$x y _ { 1 } = x ^ { 2 }$$

Solve for y_1 (complex solution)

$$\left\{\begin{matrix}\\y_{1}=x\text{, }&\text{unconditionally}\\y_{1}\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$xy_{1}=x^{2}$$

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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

Divide x^{2} by x.

$$y_{1}=x$$

Solve for y_1

$$\left\{\begin{matrix}\\y_{1}=x\text{, }&\text{unconditionally}\\y_{1}\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$xy_{1}=x^{2}$$

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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

Divide x^{2} by x.

$$y_{1}=x$$

Solve for x

$$x=y_{1}$$

$$x=0$$