Solve sqrt{2}x-sqrt{5}y=16

$$\sqrt { 2 } x - \sqrt { 5 } y = 16$$

Solve for x

$$x=\frac{\sqrt{2}\left(\sqrt{5}y+16\right)}{2}$$

Steps for Solving Linear Equation

Add \sqrt{5}y to both sides.

$$\sqrt{2}x=16+\sqrt{5}y$$

The equation is in standard form.

$$\sqrt{2}x=\sqrt{5}y+16$$

Divide both sides by \sqrt{2}.

$$\frac{\sqrt{2}x}{\sqrt{2}}=\frac{\sqrt{5}y+16}{\sqrt{2}}$$

Dividing by \sqrt{2} undoes the multiplication by \sqrt{2}.

$$x=\frac{\sqrt{5}y+16}{\sqrt{2}}$$

Divide 16+\sqrt{5}y by \sqrt{2}.

$$x=\frac{\sqrt{2}\left(\sqrt{5}y+16\right)}{2}$$

Solve for y

$$y=\frac{\sqrt{5}\left(\sqrt{2}x-16\right)}{5}$$

Steps for Solving Linear Equation

Subtract \sqrt{2}x from both sides.

$$-\sqrt{5}y=16-\sqrt{2}x$$

The equation is in standard form.

$$\left(-\sqrt{5}\right)y=-\sqrt{2}x+16$$

Divide both sides by -\sqrt{5}.

$$\frac{\left(-\sqrt{5}\right)y}{-\sqrt{5}}=\frac{-\sqrt{2}x+16}{-\sqrt{5}}$$

Dividing by -\sqrt{5} undoes the multiplication by -\sqrt{5}.

$$y=\frac{-\sqrt{2}x+16}{-\sqrt{5}}$$

Divide 16-\sqrt{2}x by -\sqrt{5}.

$$y=\frac{\sqrt{10}x-16\sqrt{5}}{5}$$