Solve sqrt{2}=x/y

$$\sqrt{ 2 } = \frac{ x }{ y }$$

Solve for x

$$x=\sqrt{2}y$$

$$y\neq 0$$

Solution Steps

Multiply both sides of the equation by y.

$$y\sqrt{2}=x$$

Swap sides so that all variable terms are on the left hand side.

$$x=y\sqrt{2}$$

Solve for y

$$y=\frac{\sqrt{2}x}{2}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by y.

$$y\sqrt{2}=x$$

The equation is in standard form.

$$\sqrt{2}y=x$$

Divide both sides by \sqrt{2}.

$$\frac{\sqrt{2}y}{\sqrt{2}}=\frac{x}{\sqrt{2}}$$

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

$$y=\frac{x}{\sqrt{2}}$$

Divide x by \sqrt{2}.

$$y=\frac{\sqrt{2}x}{2}$$

Variable y cannot be equal to 0.

$$y=\frac{\sqrt{2}x}{2}\text{, }y\neq 0$$