Solve 4x=5y+zx

$$4x=5y+zx$$

Solve for x

$$\left\{\begin{matrix}x=\frac{5y}{4-z}\text{, }&z\neq 4\\x\in \mathrm{R}\text{, }&y=0\text{ and }z=4\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract zx from both sides.

$$4x-zx=5y$$

Combine all terms containing x.

$$\left(4-z\right)x=5y$$

Divide both sides by -z+4.

$$\frac{\left(4-z\right)x}{4-z}=\frac{5y}{4-z}$$

Dividing by -z+4 undoes the multiplication by -z+4.

$$x=\frac{5y}{4-z}$$

Solve for y

$$y=-\frac{x\left(z-4\right)}{5}$$

Steps for Solving Linear Equation

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

$$5y+zx=4x$$

Subtract zx from both sides.

$$5y=4x-zx$$

The equation is in standard form.

$$5y=4x-xz$$

Divide both sides by 5.

$$\frac{5y}{5}=\frac{x\left(4-z\right)}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$y=\frac{x\left(4-z\right)}{5}$$

Divide x\left(4-z\right) by 5.

$$y=\frac{4x-xz}{5}$$