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

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

Solve for x

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

Steps for Solving Linear Equation

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

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

Subtract \frac{\sqrt{3}}{3} from both sides.

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

Multiply both sides of the equation by 3.

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

Multiply 3 and -1 to get -3.

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

The equation is in standard form.

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

Divide both sides by -3\sqrt{3}.

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

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

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

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

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

Solve for y

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

Solution Steps

Reorder the terms.

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