Solve x/y+z=4z

$$\frac{ x }{ y } +z=4z$$

Solve for x

$$x=3yz$$

$$y\neq 0$$

Solution Steps

Multiply both sides of the equation by y.

$$x+yz=4zy$$

Subtract yz from both sides.

$$x=4zy-yz$$

Combine 4zy and -yz to get 3zy.

$$x=3zy$$

Solve for y

$$\left\{\begin{matrix}y=\frac{x}{3z}\text{, }&x\neq 0\text{ and }z\neq 0\\y\neq 0\text{, }&z=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by y.

$$x+yz=4zy$$

Subtract 4zy from both sides.

$$x+yz-4zy=0$$

Combine yz and -4zy to get -3yz.

$$x-3yz=0$$

Subtract x from both sides. Anything subtracted from zero gives its negation.

$$-3yz=-x$$

The equation is in standard form.

$$\left(-3z\right)y=-x$$

Divide both sides by -3z.

$$\frac{\left(-3z\right)y}{-3z}=-\frac{x}{-3z}$$

Dividing by -3z undoes the multiplication by -3z.

$$y=-\frac{x}{-3z}$$

Divide -x by -3z.

$$y=\frac{x}{3z}$$

Variable y cannot be equal to 0.

$$y=\frac{x}{3z}\text{, }y\neq 0$$