Solve z=y-xy

$$z=y-xy$$

Solve for x (complex solution)

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

Steps for Solving Linear Equation

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

$$y-xy=z$$

Subtract y from both sides.

$$-xy=z-y$$

The equation is in standard form.

$$\left(-y\right)x=z-y$$

Divide both sides by -y.

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

Dividing by -y undoes the multiplication by -y.

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

Divide z-y by -y.

$$x=-\frac{z}{y}+1$$

Solve for y (complex solution)

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

Steps for Solving Linear Equation

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

$$y-xy=z$$

Combine all terms containing y.

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

Divide both sides by 1-x.

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

Dividing by 1-x undoes the multiplication by 1-x.

$$y=\frac{z}{1-x}$$

Solve for x

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

Steps for Solving Linear Equation

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

$$y-xy=z$$

Subtract y from both sides.

$$-xy=z-y$$

The equation is in standard form.

$$\left(-y\right)x=z-y$$

Divide both sides by -y.

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

Dividing by -y undoes the multiplication by -y.

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

Divide z-y by -y.

$$x=-\frac{z}{y}+1$$

Solve for y

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

Steps for Solving Linear Equation

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

$$y-xy=z$$

Combine all terms containing y.

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

Divide both sides by 1-x.

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

Dividing by 1-x undoes the multiplication by 1-x.

$$y=\frac{z}{1-x}$$