Solve 2y1(x-1/3)-sqrt{2}=0

$$2 y 1 ( x - \frac { 1 } { 3 } ) - \sqrt { 2 } = 0$$

Solve for x

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

$$y_{1}\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2y_{1} by x-\frac{1}{3}.

$$2y_{1}x-\frac{2}{3}y_{1}-\sqrt{2}=0$$

Add \frac{2}{3}y_{1} to both sides. Anything plus zero gives itself.

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

Add \sqrt{2} to both sides.

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

The equation is in standard form.

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

Divide both sides by 2y_{1}.

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

Dividing by 2y_{1} undoes the multiplication by 2y_{1}.

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

Divide \frac{2y_{1}}{3}+\sqrt{2} by 2y_{1}.

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

Solve for y_1

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

$$x\neq \frac{1}{3}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2y_{1} by x-\frac{1}{3}.

$$2y_{1}x-\frac{2}{3}y_{1}-\sqrt{2}=0$$

Add \sqrt{2} to both sides. Anything plus zero gives itself.

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

Combine all terms containing y_{1}.

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

Divide both sides by 2x-\frac{2}{3}.

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

Dividing by 2x-\frac{2}{3} undoes the multiplication by 2x-\frac{2}{3}.

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

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

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