Solve 9sqrt{58}a-3sqrt{58}+sqrt{58}b=9sqrt{10}a-21sqrt{10}+3sqrt{10}b

$$9 \sqrt { 58 } a - 3 \sqrt { 58 } + \sqrt { 58 } b = 9 \sqrt { 10 } a - 21 \sqrt { 10 } + 3 \sqrt { 10 } b$$

Solve for a

$$a=\frac{-\sqrt{145}\left(9-b\right)-7b-9}{108}$$

Steps for Solving Linear Equation

Subtract 9\sqrt{10}a from both sides.

$$9\sqrt{58}a-3\sqrt{58}+\sqrt{58}b-9\sqrt{10}a=-21\sqrt{10}+3\sqrt{10}b$$

Add 3\sqrt{58} to both sides.

$$9\sqrt{58}a+\sqrt{58}b-9\sqrt{10}a=-21\sqrt{10}+3\sqrt{10}b+3\sqrt{58}$$

Subtract \sqrt{58}b from both sides.

$$9\sqrt{58}a-9\sqrt{10}a=-21\sqrt{10}+3\sqrt{10}b+3\sqrt{58}-\sqrt{58}b$$

Combine all terms containing a.

$$\left(9\sqrt{58}-9\sqrt{10}\right)a=-21\sqrt{10}+3\sqrt{10}b+3\sqrt{58}-\sqrt{58}b$$

The equation is in standard form.

$$\left(9\sqrt{58}-9\sqrt{10}\right)a=3\sqrt{10}b-\sqrt{58}b+3\sqrt{58}-21\sqrt{10}$$

Divide both sides by 9\sqrt{58}-9\sqrt{10}.

$$\frac{\left(9\sqrt{58}-9\sqrt{10}\right)a}{9\sqrt{58}-9\sqrt{10}}=\frac{3\sqrt{10}b-\sqrt{58}b+3\sqrt{58}-21\sqrt{10}}{9\sqrt{58}-9\sqrt{10}}$$

Dividing by 9\sqrt{58}-9\sqrt{10} undoes the multiplication by 9\sqrt{58}-9\sqrt{10}.

$$a=\frac{3\sqrt{10}b-\sqrt{58}b+3\sqrt{58}-21\sqrt{10}}{9\sqrt{58}-9\sqrt{10}}$$

Divide -21\sqrt{10}+3\sqrt{10}b+3\sqrt{58}-\sqrt{58}b by 9\sqrt{58}-9\sqrt{10}.

$$a=\frac{\sqrt{145}b}{108}-\frac{7b}{108}-\frac{\sqrt{145}}{12}-\frac{1}{12}$$

Solve for b

$$b=\frac{9\sqrt{145}a}{8}+\frac{63a}{8}+\frac{3\sqrt{145}}{4}+\frac{57}{4}$$

Steps for Solving Linear Equation

Subtract 3\sqrt{10}b from both sides.

$$9\sqrt{58}a-3\sqrt{58}+\sqrt{58}b-3\sqrt{10}b=9\sqrt{10}a-21\sqrt{10}$$

Subtract 9\sqrt{58}a from both sides.

$$-3\sqrt{58}+\sqrt{58}b-3\sqrt{10}b=9\sqrt{10}a-21\sqrt{10}-9\sqrt{58}a$$

Add 3\sqrt{58} to both sides.

$$\sqrt{58}b-3\sqrt{10}b=9\sqrt{10}a-21\sqrt{10}-9\sqrt{58}a+3\sqrt{58}$$

Combine all terms containing b.

$$\left(\sqrt{58}-3\sqrt{10}\right)b=9\sqrt{10}a-21\sqrt{10}-9\sqrt{58}a+3\sqrt{58}$$

The equation is in standard form.

$$\left(\sqrt{58}-3\sqrt{10}\right)b=9\sqrt{10}a-9\sqrt{58}a+3\sqrt{58}-21\sqrt{10}$$

Divide both sides by \sqrt{58}-3\sqrt{10}.

$$\frac{\left(\sqrt{58}-3\sqrt{10}\right)b}{\sqrt{58}-3\sqrt{10}}=\frac{9\sqrt{10}a-9\sqrt{58}a+3\sqrt{58}-21\sqrt{10}}{\sqrt{58}-3\sqrt{10}}$$

Dividing by \sqrt{58}-3\sqrt{10} undoes the multiplication by \sqrt{58}-3\sqrt{10}.

$$b=\frac{9\sqrt{10}a-9\sqrt{58}a+3\sqrt{58}-21\sqrt{10}}{\sqrt{58}-3\sqrt{10}}$$

Divide 9\sqrt{10}a-21\sqrt{10}-9\sqrt{58}a+3\sqrt{58} by \sqrt{58}-3\sqrt{10}.

$$b=\frac{9\sqrt{145}a}{8}+\frac{63a}{8}+\frac{3\sqrt{145}}{4}+\frac{57}{4}$$