Solve x=2y+1/3y-1

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

Solve for y

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

$$x\neq \frac{2}{3}$$

Steps for Solving Linear Equation

Variable y cannot be equal to \frac{1}{3} since division by zero is not defined. Multiply both sides of the equation by 3y-1.

$$x\left(3y-1\right)=2y+1$$

Use the distributive property to multiply x by 3y-1.

$$3xy-x=2y+1$$

Subtract 2y from both sides.

$$3xy-x-2y=1$$

Add x to both sides.

$$3xy-2y=1+x$$

Combine all terms containing y.

$$\left(3x-2\right)y=1+x$$

The equation is in standard form.

$$\left(3x-2\right)y=x+1$$

Divide both sides by 3x-2.

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

Dividing by 3x-2 undoes the multiplication by 3x-2.

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

Variable y cannot be equal to \frac{1}{3}.

$$y=\frac{x+1}{3x-2}\text{, }y\neq \frac{1}{3}$$

Solve for x

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

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