Solve x=2xy+1

$$x = 2 x y + 1$$

Solve for x

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

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

Steps for Solving Linear Equation

Subtract 2xy from both sides.

$$x-2xy=1$$

Combine all terms containing x.

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

Divide both sides by -2y+1.

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

Dividing by -2y+1 undoes the multiplication by -2y+1.

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

Solve for y

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

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$2xy+1=x$$

Subtract 1 from both sides.

$$2xy=x-1$$

Divide both sides by 2x.

$$\frac{2xy}{2x}=\frac{x-1}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

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

Divide x-1 by 2x.

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