Solve y=zx-3/x-1

$$y = \frac { z x - 3 } { x - 1 }$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{3-y}{y-z}\text{, }&z\neq 3\text{ and }y\neq z\\x\neq 1\text{, }&y=3\text{ and }z=3\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by x-1.

$$y\left(x-1\right)=zx-3$$

Use the distributive property to multiply y by x-1.

$$yx-y=zx-3$$

Subtract zx from both sides.

$$yx-y-zx=-3$$

Add y to both sides.

$$yx-zx=-3+y$$

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by y-z.

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

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

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

Variable x cannot be equal to 1.

$$x=\frac{y-3}{y-z}\text{, }x\neq 1$$

Solve for y

$$y=-\frac{3-xz}{x-1}$$

$$x\neq 1$$