Solve xy=z(2-y)

$$xy=z(2-y)$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{z\left(y-2\right)}{y}\text{, }&y\neq 0\\x\in \mathrm{C}\text{, }&z=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply z by 2-y.

$$xy=2z-zy$$

The equation is in standard form.

$$yx=2z-yz$$

Divide both sides by y.

$$\frac{yx}{y}=\frac{z\left(2-y\right)}{y}$$

Dividing by y undoes the multiplication by y.

$$x=\frac{z\left(2-y\right)}{y}$$

Solve for y (complex solution)

$$\left\{\begin{matrix}y=\frac{2z}{x+z}\text{, }&x\neq -z\\y\in \mathrm{C}\text{, }&z=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply z by 2-y.

$$xy=2z-zy$$

Add zy to both sides.

$$xy+zy=2z$$

Combine all terms containing y.

$$\left(x+z\right)y=2z$$

Divide both sides by x+z.

$$\frac{\left(x+z\right)y}{x+z}=\frac{2z}{x+z}$$

Dividing by x+z undoes the multiplication by x+z.

$$y=\frac{2z}{x+z}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{z\left(y-2\right)}{y}\text{, }&y\neq 0\\x\in \mathrm{R}\text{, }&z=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply z by 2-y.

$$xy=2z-zy$$

The equation is in standard form.

$$yx=2z-yz$$

Divide both sides by y.

$$\frac{yx}{y}=\frac{z\left(2-y\right)}{y}$$

Dividing by y undoes the multiplication by y.

$$x=\frac{z\left(2-y\right)}{y}$$

Solve for y

$$\left\{\begin{matrix}y=\frac{2z}{x+z}\text{, }&x\neq -z\\y\in \mathrm{R}\text{, }&z=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply z by 2-y.

$$xy=2z-zy$$

Add zy to both sides.

$$xy+zy=2z$$

Combine all terms containing y.

$$\left(x+z\right)y=2z$$

Divide both sides by x+z.

$$\frac{\left(x+z\right)y}{x+z}=\frac{2z}{x+z}$$

Dividing by x+z undoes the multiplication by x+z.

$$y=\frac{2z}{x+z}$$