Solve y=1-yx/z

$$y= \frac{ 1-yx }{ z }$$

Solve for x

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

$$y\neq 0\text{ and }z\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by z.

$$yz=1-yx$$

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

$$1-yx=yz$$

Subtract 1 from both sides.

$$-yx=yz-1$$

The equation is in standard form.

$$\left(-y\right)x=yz-1$$

Divide both sides by -y.

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

Dividing by -y undoes the multiplication by -y.

$$x=\frac{yz-1}{-y}$$

Divide yz-1 by -y.

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

Solve for y

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

$$x\neq -z\text{ and }z\neq 0$$

Steps for Solving Linear Equation

Subtract \frac{1-yx}{z} from both sides.

$$y-\frac{1-yx}{z}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply y times \frac{z}{z}.

$$\frac{yz}{z}-\frac{1-yx}{z}=0$$

Since \frac{yz}{z} and \frac{1-yx}{z} have the same denominator, subtract them by subtracting their numerators.

$$\frac{yz-\left(1-yx\right)}{z}=0$$

Do the multiplications in yz-\left(1-yx\right).

$$\frac{yz-1+xy}{z}=0$$

Multiply both sides of the equation by z.

$$yz-1+xy=0$$

Add 1 to both sides. Anything plus zero gives itself.

$$yz+xy=1$$

Combine all terms containing y.

$$\left(z+x\right)y=1$$

The equation is in standard form.

$$\left(x+z\right)y=1$$

Divide both sides by z+x.

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

Dividing by z+x undoes the multiplication by z+x.

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