Solve a/x=y/5+y

$$\frac { a } { x } = \frac { y } { 5 + y }$$

Solve for a

$$a=\frac{xy}{y+5}$$

$$x\neq 0\text{ and }y\neq -5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x\left(y+5\right), the least common multiple of x,5+y.

$$\left(y+5\right)a=xy$$

Divide both sides by 5+y.

$$\frac{\left(y+5\right)a}{y+5}=\frac{xy}{y+5}$$

Dividing by 5+y undoes the multiplication by 5+y.

$$a=\frac{xy}{y+5}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{a\left(y+5\right)}{y}\text{, }&y\neq -5\text{ and }a\neq 0\text{ and }y\neq 0\\x\neq 0\text{, }&a=0\text{ and }y=0\end{matrix}\right.$$

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 x\left(y+5\right), the least common multiple of x,5+y.

$$\left(y+5\right)a=xy$$

Use the distributive property to multiply y+5 by a.

$$ya+5a=xy$$

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

$$xy=ya+5a$$

The equation is in standard form.

$$yx=ay+5a$$

Divide both sides by y.

$$\frac{yx}{y}=\frac{a\left(y+5\right)}{y}$$

Dividing by y undoes the multiplication by y.

$$x=\frac{a\left(y+5\right)}{y}$$

Variable x cannot be equal to 0.

$$x=\frac{a\left(y+5\right)}{y}\text{, }x\neq 0$$