Solve 3/sqrt{2}x-2y=1

$$\frac { 3 } { \sqrt { 2 } } x - 2 y = 1$$

Solve for x

$$x=\frac{\sqrt{2}\left(2y+1\right)}{3}$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{3}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{3\sqrt{2}}{\left(\sqrt{2}\right)^{2}}x-2y=1$$

The square of \sqrt{2} is 2.

$$\frac{3\sqrt{2}}{2}x-2y=1$$

Express \frac{3\sqrt{2}}{2}x as a single fraction.

$$\frac{3\sqrt{2}x}{2}-2y=1$$

Add 2y to both sides.

$$\frac{3\sqrt{2}x}{2}=1+2y$$

Multiply both sides of the equation by 2.

$$3\sqrt{2}x=2+4y$$

The equation is in standard form.

$$3\sqrt{2}x=4y+2$$

Divide both sides by 3\sqrt{2}.

$$\frac{3\sqrt{2}x}{3\sqrt{2}}=\frac{4y+2}{3\sqrt{2}}$$

Dividing by 3\sqrt{2} undoes the multiplication by 3\sqrt{2}.

$$x=\frac{4y+2}{3\sqrt{2}}$$

Divide 2+4y by 3\sqrt{2}.

$$x=\frac{\sqrt{2}\left(2y+1\right)}{3}$$

Solve for y

$$y=\frac{3\sqrt{2}x}{4}-\frac{1}{2}$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{3}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{3\sqrt{2}}{\left(\sqrt{2}\right)^{2}}x-2y=1$$

The square of \sqrt{2} is 2.

$$\frac{3\sqrt{2}}{2}x-2y=1$$

Express \frac{3\sqrt{2}}{2}x as a single fraction.

$$\frac{3\sqrt{2}x}{2}-2y=1$$

Subtract \frac{3\sqrt{2}x}{2} from both sides.

$$-2y=1-\frac{3\sqrt{2}x}{2}$$

Multiply both sides of the equation by 2.

$$-4y=2-3\sqrt{2}x$$

The equation is in standard form.

$$-4y=-3\sqrt{2}x+2$$

Divide both sides by -4.

$$\frac{-4y}{-4}=\frac{-3\sqrt{2}x+2}{-4}$$

Dividing by -4 undoes the multiplication by -4.

$$y=\frac{-3\sqrt{2}x+2}{-4}$$

Divide 2-3\sqrt{2}x by -4.

$$y=\frac{3\sqrt{2}x}{4}-\frac{1}{2}$$