Solve x=2y+1/6y-3

$$x= \frac{ 2y+1 }{ 6y-3 }$$

Solve for y

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

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

Steps for Solving Linear Equation

Variable y cannot be equal to \frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by 3\left(2y-1\right).

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

Use the distributive property to multiply x\times 3 by 2y-1.

$$6xy-x\times 3=2y+1$$

Multiply -1 and 3 to get -3.

$$6xy-3x=2y+1$$

Subtract 2y from both sides.

$$6xy-3x-2y=1$$

Add 3x to both sides.

$$6xy-2y=1+3x$$

Combine all terms containing y.

$$\left(6x-2\right)y=1+3x$$

The equation is in standard form.

$$\left(6x-2\right)y=3x+1$$

Divide both sides by 6x-2.

$$\frac{\left(6x-2\right)y}{6x-2}=\frac{3x+1}{6x-2}$$

Dividing by 6x-2 undoes the multiplication by 6x-2.

$$y=\frac{3x+1}{6x-2}$$

Divide 3x+1 by 6x-2.

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

Variable y cannot be equal to \frac{1}{2}.

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

Solve for x

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

$$y\neq \frac{1}{2}$$