Solve x+y=2xy

$$x + y = 2 x y$$

Solve for x

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

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

Steps for Solving Linear Equation

Subtract 2xy from both sides.

$$x+y-2xy=0$$

Subtract y from both sides. Anything subtracted from zero gives its negation.

$$x-2xy=-y$$

Combine all terms containing x.

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

Divide both sides by 1-2y.

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

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

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

Solve for y

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

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

Steps for Solving Linear Equation

Subtract 2xy from both sides.

$$x+y-2xy=0$$

Subtract x from both sides. Anything subtracted from zero gives its negation.

$$y-2xy=-x$$

Combine all terms containing y.

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

Divide both sides by 1-2x.

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

Dividing by 1-2x undoes the multiplication by 1-2x.

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