Solve 1y/3x=z/y

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

Solve for x

$$x=\frac{y^{2}}{3z}$$

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

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 3xy, the least common multiple of 3x,y.

$$y\times 1y=3xz$$

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

$$y^{2}\times 1=3xz$$

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

$$3xz=y^{2}\times 1$$

Reorder the terms.

$$3xz=y^{2}$$

The equation is in standard form.

$$3zx=y^{2}$$

Divide both sides by 3z.

$$\frac{3zx}{3z}=\frac{y^{2}}{3z}$$

Dividing by 3z undoes the multiplication by 3z.

$$x=\frac{y^{2}}{3z}$$

Variable x cannot be equal to 0.

$$x=\frac{y^{2}}{3z}\text{, }x\neq 0$$

Solve for y

$$y=\sqrt{3xz}$$

$$y=-\sqrt{3xz}\text{, }\left(z<0\text{ and }x<0\right)\text{ or }\left(x>0\text{ and }z>0\right)$$