Solve y=a/frac{x{3}}

$$y = \frac { a } { \frac { x } { 3 } }$$

Solve for a

$$a=\frac{xy}{3}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Divide a by \frac{x}{3} by multiplying a by the reciprocal of \frac{x}{3}.

$$y=\frac{a\times 3}{x}$$

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

$$\frac{a\times 3}{x}=y$$

Multiply both sides of the equation by x.

$$a\times 3=yx$$

The equation is in standard form.

$$3a=xy$$

Divide both sides by 3.

$$\frac{3a}{3}=\frac{xy}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$a=\frac{xy}{3}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{3a}{y}\text{, }&a\neq 0\text{ and }y\neq 0\\x\neq 0\text{, }&y=0\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Divide a by \frac{x}{3} by multiplying a by the reciprocal of \frac{x}{3}.

$$y=\frac{a\times 3}{x}$$

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

$$\frac{a\times 3}{x}=y$$

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$a\times 3=yx$$

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

$$yx=a\times 3$$

The equation is in standard form.

$$yx=3a$$

Divide both sides by y.

$$\frac{yx}{y}=\frac{3a}{y}$$

Dividing by y undoes the multiplication by y.

$$x=\frac{3a}{y}$$

Variable x cannot be equal to 0.

$$x=\frac{3a}{y}\text{, }x\neq 0$$