Solve sqrt{3}a-a+2b=3+sqrt{3}

$$\sqrt { 3 } a - a + 2 b = 3 + \sqrt { 3 }$$

Solve for a

$$a=-\sqrt{3}b-b+2\sqrt{3}+3$$

Steps for Solving Linear Equation

Subtract 2b from both sides.

$$\sqrt{3}a-a=3+\sqrt{3}-2b$$

Combine all terms containing a.

$$\left(\sqrt{3}-1\right)a=3+\sqrt{3}-2b$$

The equation is in standard form.

$$\left(\sqrt{3}-1\right)a=-2b+\sqrt{3}+3$$

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

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

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

$$a=\frac{-2b+\sqrt{3}+3}{\sqrt{3}-1}$$

Divide 3+\sqrt{3}-2b by \sqrt{3}-1.

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

Solve for b

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

Steps for Solving Linear Equation

Subtract \sqrt{3}a from both sides.

$$-a+2b=3+\sqrt{3}-\sqrt{3}a$$

Add a to both sides.

$$2b=3+\sqrt{3}-\sqrt{3}a+a$$

Reorder the terms.

$$2b=-\sqrt{3}a+a+\sqrt{3}+3$$

Divide both sides by 2.

$$\frac{2b}{2}=\frac{-\sqrt{3}a+a+\sqrt{3}+3}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$b=\frac{-\sqrt{3}a+a+\sqrt{3}+3}{2}$$