Solve x:y=2:3

$$x : y = 2 : 3$$

Solve for x

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

$$y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3y, the least common multiple of y,3.

$$3x=2y$$

Divide both sides by 3.

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

Dividing by 3 undoes the multiplication by 3.

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

Solve for y

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

$$x\neq 0$$

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 3y, the least common multiple of y,3.

$$3x=2y$$

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

$$2y=3x$$

Divide both sides by 2.

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

Dividing by 2 undoes the multiplication by 2.

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

Variable y cannot be equal to 0.

$$y=\frac{3x}{2}\text{, }y\neq 0$$