Solve 1/x+0/y=y/z

$$\frac { 1 } { x } + \frac { 0 } { y } = \frac { y } { z }$$

Solve for x

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

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

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by xyz, the least common multiple of x,y,z.

$$yz+xz\times 0=xyy$$

Anything times zero gives zero.

$$yz+0=xyy$$

Anything plus zero gives itself.

$$yz=xyy$$

Multiply y and y to get y^{2}.

$$yz=xy^{2}$$

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

$$xy^{2}=yz$$

The equation is in standard form.

$$y^{2}x=yz$$

Divide both sides by y^{2}.

$$\frac{y^{2}x}{y^{2}}=\frac{yz}{y^{2}}$$

Dividing by y^{2} undoes the multiplication by y^{2}.

$$x=\frac{yz}{y^{2}}$$

Divide yz by y^{2}.

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

Variable x cannot be equal to 0.

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

Solve for y

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

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