Solve x=x+x+xy

$$x=x+x+xy$$

Solve for x (complex solution)

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

Steps for Solving Linear Equation

Combine x and x to get 2x.

$$x=2x+xy$$

Subtract 2x from both sides.

$$x-2x=xy$$

Combine x and -2x to get -x.

$$-x=xy$$

Subtract xy from both sides.

$$-x-xy=0$$

Combine all terms containing x.

$$\left(-1-y\right)x=0$$

The equation is in standard form.

$$\left(-y-1\right)x=0$$

Divide 0 by -1-y.

$$x=0$$

Solve for y (complex solution)

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

Steps for Solving Linear Equation

Combine x and x to get 2x.

$$x=2x+xy$$

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

$$2x+xy=x$$

Subtract 2x from both sides.

$$xy=x-2x$$

Combine x and -2x to get -x.

$$xy=-x$$

Divide both sides by x.

$$\frac{xy}{x}=-\frac{x}{x}$$

Dividing by x undoes the multiplication by x.

$$y=-\frac{x}{x}$$

Divide -x by x.

$$y=-1$$

Solve for x

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

Steps for Solving Linear Equation

Combine x and x to get 2x.

$$x=2x+xy$$

Subtract 2x from both sides.

$$x-2x=xy$$

Combine x and -2x to get -x.

$$-x=xy$$

Subtract xy from both sides.

$$-x-xy=0$$

Combine all terms containing x.

$$\left(-1-y\right)x=0$$

The equation is in standard form.

$$\left(-y-1\right)x=0$$

Divide 0 by -1-y.

$$x=0$$

Solve for y

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

Steps for Solving Linear Equation

Combine x and x to get 2x.

$$x=2x+xy$$

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

$$2x+xy=x$$

Subtract 2x from both sides.

$$xy=x-2x$$

Combine x and -2x to get -x.

$$xy=-x$$

Divide both sides by x.

$$\frac{xy}{x}=-\frac{x}{x}$$

Dividing by x undoes the multiplication by x.

$$y=-\frac{x}{x}$$

Divide -x by x.

$$y=-1$$