Solve z/y+varepsilon=u

$$\frac { z } { y } + \varepsilon = u$$

Solve for u

$$u=\epsilon +\frac{z}{y}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y.

$$z+y\epsilon =uy$$

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

$$uy=z+y\epsilon$$

The equation is in standard form.

$$yu=y\epsilon +z$$

Divide both sides by y.

$$\frac{yu}{y}=\frac{y\epsilon +z}{y}$$

Dividing by y undoes the multiplication by y.

$$u=\frac{y\epsilon +z}{y}$$

Divide \epsilon y+z by y.

$$u=\epsilon +\frac{z}{y}$$

Solve for y

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

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.

$$z+y\epsilon =uy$$

Subtract uy from both sides.

$$z+y\epsilon -uy=0$$

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

$$y\epsilon -uy=-z$$

Combine all terms containing y.

$$\left(\epsilon -u\right)y=-z$$

Divide both sides by \epsilon -u.

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

Dividing by \epsilon -u undoes the multiplication by \epsilon -u.

$$y=-\frac{z}{\epsilon -u}$$

Variable y cannot be equal to 0.

$$y=-\frac{z}{\epsilon -u}\text{, }y\neq 0$$