Solve 3y=sqrt{3}x+3-2sqrt{3}

$$3 y = \sqrt { 3 } x + 3 - 2 \sqrt { 3 }$$

Solve for x

$$x=\sqrt{3}y+2-\sqrt{3}$$

Steps for Solving Linear Equation

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

$$\sqrt{3}x+3-2\sqrt{3}=3y$$

Subtract 3 from both sides.

$$\sqrt{3}x-2\sqrt{3}=3y-3$$

Add 2\sqrt{3} to both sides.

$$\sqrt{3}x=3y-3+2\sqrt{3}$$

The equation is in standard form.

$$\sqrt{3}x=3y+2\sqrt{3}-3$$

Divide both sides by \sqrt{3}.

$$\frac{\sqrt{3}x}{\sqrt{3}}=\frac{3y+2\sqrt{3}-3}{\sqrt{3}}$$

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

$$x=\frac{3y+2\sqrt{3}-3}{\sqrt{3}}$$

Divide 3y-3+2\sqrt{3} by \sqrt{3}.

$$x=\frac{\sqrt{3}\left(3y+2\sqrt{3}-3\right)}{3}$$

Solve for y

$$y=\frac{\sqrt{3}\left(x+\sqrt{3}-2\right)}{3}$$

Steps for Solving Linear Equation

The equation is in standard form.

$$3y=\sqrt{3}x+3-2\sqrt{3}$$

Divide both sides by 3.

$$\frac{3y}{3}=\frac{\sqrt{3}\left(x+\sqrt{3}-2\right)}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$y=\frac{\sqrt{3}\left(x+\sqrt{3}-2\right)}{3}$$