Solve xy-y^2-x+y=0

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

Solve for x (complex solution)

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

Steps for Solving Linear Equation

Add y^{2} to both sides. Anything plus zero gives itself.

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

Subtract y from both sides.

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

Combine all terms containing x.

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

Divide both sides by -1+y.

$$\frac{\left(y-1\right)x}{y-1}=\frac{y\left(y-1\right)}{y-1}$$

Dividing by -1+y undoes the multiplication by -1+y.

$$x=\frac{y\left(y-1\right)}{y-1}$$

Divide y\left(-1+y\right) by -1+y.

$$x=y$$

Solve for x

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

Steps for Solving Linear Equation

Add y^{2} to both sides. Anything plus zero gives itself.

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

Subtract y from both sides.

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

Combine all terms containing x.

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

Divide both sides by -1+y.

$$\frac{\left(y-1\right)x}{y-1}=\frac{y\left(y-1\right)}{y-1}$$

Dividing by -1+y undoes the multiplication by -1+y.

$$x=\frac{y\left(y-1\right)}{y-1}$$

Divide y\left(-1+y\right) by -1+y.

$$x=y$$

Solve for y

$$y=x$$

$$y=1$$