Solve 1=xy-x_{0}

$$1 = x y - x _ { 0 }$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{x_{0}+1}{y}\text{, }&y\neq 0\\x\in \mathrm{C}\text{, }&x_{0}=-1\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$xy-x_{0}=1$$

Add x_{0} to both sides.

$$xy=1+x_{0}$$

The equation is in standard form.

$$yx=x_{0}+1$$

Divide both sides by y.

$$\frac{yx}{y}=\frac{x_{0}+1}{y}$$

Dividing by y undoes the multiplication by y.

$$x=\frac{x_{0}+1}{y}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{x_{0}+1}{y}\text{, }&y\neq 0\\x\in \mathrm{R}\text{, }&x_{0}=-1\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$xy-x_{0}=1$$

Add x_{0} to both sides.

$$xy=1+x_{0}$$

The equation is in standard form.

$$yx=x_{0}+1$$

Divide both sides by y.

$$\frac{yx}{y}=\frac{x_{0}+1}{y}$$

Dividing by y undoes the multiplication by y.

$$x=\frac{x_{0}+1}{y}$$

Solve for x_0

$$x_{0}=xy-1$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$xy-x_{0}=1$$

Subtract xy from both sides.

$$-x_{0}=1-xy$$

Divide both sides by -1.

$$\frac{-x_{0}}{-1}=\frac{1-xy}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x_{0}=\frac{1-xy}{-1}$$

Divide 1-xy by -1.

$$x_{0}=xy-1$$