Solve 2/4=2/3x/y

$$\frac{ 2 }{ 4 } = \frac{ 2 }{ 3 } \frac{ x }{ y }$$

Solve for x

$$x=\frac{3y}{4}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12y, the least common multiple of 4,3,y.

$$3y\times 2=\frac{2}{3}\times 12x$$

Multiply 3 and 2 to get 6.

$$6y=\frac{2}{3}\times 12x$$

Multiply \frac{2}{3} and 12 to get 8.

$$6y=8x$$

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

$$8x=6y$$

Divide both sides by 8.

$$\frac{8x}{8}=\frac{6y}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$x=\frac{6y}{8}$$

Divide 6y by 8.

$$x=\frac{3y}{4}$$

Solve for y

$$y=\frac{4x}{3}$$

$$x\neq 0$$

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 12y, the least common multiple of 4,3,y.

$$3y\times 2=\frac{2}{3}\times 12x$$

Multiply 3 and 2 to get 6.

$$6y=\frac{2}{3}\times 12x$$

Multiply \frac{2}{3} and 12 to get 8.

$$6y=8x$$

Divide both sides by 6.

$$\frac{6y}{6}=\frac{8x}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$y=\frac{8x}{6}$$

Divide 8x by 6.

$$y=\frac{4x}{3}$$

Variable y cannot be equal to 0.

$$y=\frac{4x}{3}\text{, }y\neq 0$$