Solve 500xy^2/xy=n

$$\frac { 500 x y ^ { 2 } } { x y } = n$$

Solve for n

$$n=500y$$

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

Steps for Solving Linear Equation

Multiply both sides of the equation by xy.

$$500xy^{2}=nxy$$

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

$$nxy=500xy^{2}$$

The equation is in standard form.

$$xyn=500xy^{2}$$

Divide both sides by xy.

$$\frac{xyn}{xy}=\frac{500xy^{2}}{xy}$$

Dividing by xy undoes the multiplication by xy.

$$n=\frac{500xy^{2}}{xy}$$

Divide 500xy^{2} by xy.

$$n=500y$$

Solve for x

$$x\neq 0$$

$$n=500y\text{ and }y\neq 0$$

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 xy.

$$500xy^{2}=nxy$$

Subtract nxy from both sides.

$$500xy^{2}-nxy=0$$

Combine all terms containing x.

$$\left(500y^{2}-ny\right)x=0$$

Divide 0 by 500y^{2}-ny.

$$x=0$$

Variable x cannot be equal to 0.

$$x\in \emptyset$$