Solve y=1/sqrt{3}(x-3)+3-sqrt{3}

$$y = \frac { 1 } { \sqrt { 3 } } ( x - 3 ) + 3 - \sqrt { 3 }$$

Solve for x

$$x=\sqrt{3}y+6-3\sqrt{3}$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

Express \frac{\sqrt{3}}{3}\left(x-3\right) as a single fraction.

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

Use the distributive property to multiply \sqrt{3} by x-3.

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

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

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

Subtract 3 from both sides.

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

Add \sqrt{3} to both sides.

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

Multiply both sides of the equation by 3.

$$\sqrt{3}x-3\sqrt{3}=3y-9+3\sqrt{3}$$

Add 3\sqrt{3} to both sides.

$$\sqrt{3}x=3y-9+3\sqrt{3}+3\sqrt{3}$$

Combine 3\sqrt{3} and 3\sqrt{3} to get 6\sqrt{3}.

$$\sqrt{3}x=3y-9+6\sqrt{3}$$

The equation is in standard form.

$$\sqrt{3}x=3y+6\sqrt{3}-9$$

Divide both sides by \sqrt{3}.

$$\frac{\sqrt{3}x}{\sqrt{3}}=\frac{3y+6\sqrt{3}-9}{\sqrt{3}}$$

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

$$x=\frac{3y+6\sqrt{3}-9}{\sqrt{3}}$$

Divide 3y-9+6\sqrt{3} by \sqrt{3}.

$$x=\sqrt{3}y+6-3\sqrt{3}$$

Solve for y

$$y=\frac{\sqrt{3}x+9-6\sqrt{3}}{3}$$