Solve xy=2(x+y)

$$xy=2(x+y)$$

Solve for x

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

$$y\neq 2$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by x+y.

$$xy=2x+2y$$

Subtract 2x from both sides.

$$xy-2x=2y$$

Combine all terms containing x.

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

Divide both sides by y-2.

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

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

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

Solve for y

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

$$x\neq 2$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by x+y.

$$xy=2x+2y$$

Subtract 2y from both sides.

$$xy-2y=2x$$

Combine all terms containing y.

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

Divide both sides by x-2.

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

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

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