Solve z=x-5xy

$$z=x-5xy$$

Solve for x

$$\left\{\begin{matrix}x=\frac{z}{1-5y}\text{, }&y\neq \frac{1}{5}\\x\in \mathrm{R}\text{, }&z=0\text{ and }y=\frac{1}{5}\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$x-5xy=z$$

Combine all terms containing x.

$$\left(1-5y\right)x=z$$

Divide both sides by 1-5y.

$$\frac{\left(1-5y\right)x}{1-5y}=\frac{z}{1-5y}$$

Dividing by 1-5y undoes the multiplication by 1-5y.

$$x=\frac{z}{1-5y}$$

Solve for y

$$\left\{\begin{matrix}y=-\frac{z}{5x}+\frac{1}{5}\text{, }&x\neq 0\\y\in \mathrm{R}\text{, }&z=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$x-5xy=z$$

Subtract x from both sides.

$$-5xy=z-x$$

The equation is in standard form.

$$\left(-5x\right)y=z-x$$

Divide both sides by -5x.

$$\frac{\left(-5x\right)y}{-5x}=\frac{z-x}{-5x}$$

Dividing by -5x undoes the multiplication by -5x.

$$y=\frac{z-x}{-5x}$$

Divide z-x by -5x.

$$y=-\frac{z}{5x}+\frac{1}{5}$$