Solve xy=2x-y

$$xy=2x-y$$

Solve for x

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

$$y\neq 2$$

Steps for Solving Linear Equation

Subtract 2x from both sides.

$$xy-2x=-y$$

Combine all terms containing x.

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

Divide both sides by y-2.

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

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

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

Solve for y

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

$$x\neq -1$$

Steps for Solving Linear Equation

Add y to both sides.

$$xy+y=2x$$

Combine all terms containing y.

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

Divide both sides by x+1.

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

Dividing by x+1 undoes the multiplication by x+1.

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