Solve sqrt{3}x+sqrt{7}y+sqrt{6}=0

$$\sqrt { 3 } x + \sqrt { 7 } y + \sqrt { 6 } = 0$$

Solve for x

$$x=\frac{-\sqrt{21}y-3\sqrt{2}}{3}$$

Steps for Solving Linear Equation

Subtract \sqrt{7}y from both sides. Anything subtracted from zero gives its negation.

$$\sqrt{3}x+\sqrt{6}=-\sqrt{7}y$$

Subtract \sqrt{6} from both sides.

$$\sqrt{3}x=-\sqrt{7}y-\sqrt{6}$$

Divide both sides by \sqrt{3}.

$$\frac{\sqrt{3}x}{\sqrt{3}}=\frac{-\sqrt{7}y-\sqrt{6}}{\sqrt{3}}$$

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

$$x=\frac{-\sqrt{7}y-\sqrt{6}}{\sqrt{3}}$$

Divide -\sqrt{7}y-\sqrt{6} by \sqrt{3}.

$$x=-\frac{\sqrt{3}\left(\sqrt{7}y+\sqrt{6}\right)}{3}$$

Solve for y

$$y=\frac{-\sqrt{21}x-\sqrt{42}}{7}$$

Steps for Solving Linear Equation

Subtract \sqrt{3}x from both sides. Anything subtracted from zero gives its negation.

$$\sqrt{7}y+\sqrt{6}=-\sqrt{3}x$$

Subtract \sqrt{6} from both sides.

$$\sqrt{7}y=-\sqrt{3}x-\sqrt{6}$$

Divide both sides by \sqrt{7}.

$$\frac{\sqrt{7}y}{\sqrt{7}}=\frac{-\sqrt{3}x-\sqrt{6}}{\sqrt{7}}$$

Dividing by \sqrt{7} undoes the multiplication by \sqrt{7}.

$$y=\frac{-\sqrt{3}x-\sqrt{6}}{\sqrt{7}}$$

Divide -\sqrt{3}x-\sqrt{6} by \sqrt{7}.

$$y=-\frac{\sqrt{7}\left(\sqrt{3}x+\sqrt{6}\right)}{7}$$