Solve 5=p/m-q/n

$$5 = \frac { p } { m } - \frac { q } { n }$$

Solve for m

$$\left\{\begin{matrix}m=\frac{np}{5n+q}\text{, }&n\neq 0\text{ and }p\neq 0\text{ and }q\neq -5n\\m\neq 0\text{, }&n\neq 0\text{ and }q=-5n\text{ and }p=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable m cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by mn, the least common multiple of m,n.

$$5mn=np-mq$$

Add mq to both sides.

$$5mn+mq=np$$

Combine all terms containing m.

$$\left(5n+q\right)m=np$$

Divide both sides by 5n+q.

$$\frac{\left(5n+q\right)m}{5n+q}=\frac{np}{5n+q}$$

Dividing by 5n+q undoes the multiplication by 5n+q.

$$m=\frac{np}{5n+q}$$

Variable m cannot be equal to 0.

$$m=\frac{np}{5n+q}\text{, }m\neq 0$$

Solve for n

$$\left\{\begin{matrix}n=-\frac{mq}{5m-p}\text{, }&m\neq 0\text{ and }q\neq 0\text{ and }p\neq 5m\\n\neq 0\text{, }&m\neq 0\text{ and }p=5m\text{ and }q=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by mn, the least common multiple of m,n.

$$5mn=np-mq$$

Subtract np from both sides.

$$5mn-np=-mq$$

Combine all terms containing n.

$$\left(5m-p\right)n=-mq$$

Divide both sides by 5m-p.

$$\frac{\left(5m-p\right)n}{5m-p}=-\frac{mq}{5m-p}$$

Dividing by 5m-p undoes the multiplication by 5m-p.

$$n=-\frac{mq}{5m-p}$$

Variable n cannot be equal to 0.

$$n=-\frac{mq}{5m-p}\text{, }n\neq 0$$