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

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

Solve for x

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

Steps for Solving Linear Equation

Use the distributive property to multiply 1-\sqrt{3} by y.

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

Subtract y from both sides.

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

Add \sqrt{3}y to both sides.

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

The equation is in standard form.

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

Divide both sides by \sqrt{3}.

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

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

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

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

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

Solve for y

$$y=\frac{\left(\sqrt{3}+1\right)\left(\sqrt{3}x-3\right)}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1-\sqrt{3} by y.

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

Subtract \sqrt{3}x from both sides.

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

Reorder the terms.

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

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by 1-\sqrt{3}.

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

Dividing by 1-\sqrt{3} undoes the multiplication by 1-\sqrt{3}.

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

Divide -\sqrt{3}x+3 by 1-\sqrt{3}.

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