Solve frac{sqrt{3}}{3}=x/3+y

$$\frac{ \sqrt{ 3 } }{ 3 } = \frac{ x }{ 3+y }$$

Solve for x

$$x=\frac{\sqrt{3}\left(y+3\right)}{3}$$

$$y\neq -3$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3\left(y+3\right), the least common multiple of 3,3+y.

$$\left(y+3\right)\sqrt{3}=3x$$

Use the distributive property to multiply y+3 by \sqrt{3}.

$$y\sqrt{3}+3\sqrt{3}=3x$$

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

$$3x=y\sqrt{3}+3\sqrt{3}$$

The equation is in standard form.

$$3x=\sqrt{3}y+3\sqrt{3}$$

Divide both sides by 3.

$$\frac{3x}{3}=\frac{\sqrt{3}\left(y+3\right)}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x=\frac{\sqrt{3}\left(y+3\right)}{3}$$

Solve for y

$$y=\sqrt{3}x-3$$

$$x\neq 0$$

Steps for Solving Linear Equation

Variable y cannot be equal to -3 since division by zero is not defined. Multiply both sides of the equation by 3\left(y+3\right), the least common multiple of 3,3+y.

$$\left(y+3\right)\sqrt{3}=3x$$

Use the distributive property to multiply y+3 by \sqrt{3}.

$$y\sqrt{3}+3\sqrt{3}=3x$$

Subtract 3\sqrt{3} from both sides.

$$y\sqrt{3}=3x-3\sqrt{3}$$

The equation is in standard form.

$$\sqrt{3}y=3x-3\sqrt{3}$$

Divide both sides by \sqrt{3}.

$$\frac{\sqrt{3}y}{\sqrt{3}}=\frac{3x-3\sqrt{3}}{\sqrt{3}}$$

Dividing by \sqrt{3} undoes the multiplication by \sqrt{3}.

$$y=\frac{3x-3\sqrt{3}}{\sqrt{3}}$$

Divide 3x-3\sqrt{3} by \sqrt{3}.

$$y=\sqrt{3}x-3$$

Variable y cannot be equal to -3.

$$y=\sqrt{3}x-3\text{, }y\neq -3$$