Solve y=3x+sqrt{3}x

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

Solve for x

$$x=-\frac{\sqrt{3}y}{6}+\frac{y}{2}$$

Steps for Solving Linear Equation

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

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

Combine all terms containing x.

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

The equation is in standard form.

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

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

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

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

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

Divide y by 3+\sqrt{3}.

$$x=-\frac{\sqrt{3}y}{6}+\frac{y}{2}$$

Solve for y

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