Solve x/y=3x^2

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

Solve for y

$$\left\{\begin{matrix}y=\frac{1}{3x}\text{, }&x\neq 0\\y\neq 0\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

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

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

Divide both sides by 3x^{2}.

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

Dividing by 3x^{2} undoes the multiplication by 3x^{2}.

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

Divide x by 3x^{2}.

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

Variable y cannot be equal to 0.

$$y=\frac{1}{3x}\text{, }y\neq 0$$

Solve for x

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

$$x=0\text{, }y\neq 0$$