Solve xy=y-2

$$x y = y - 2$$

Solve for x

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

$$y\neq 0$$

Steps for Solving Linear Equation

The equation is in standard form.

$$yx=y-2$$

Divide both sides by y.

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

Dividing by y undoes the multiplication by y.

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

Solve for y

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

$$x\neq 1$$

Steps for Solving Linear Equation

Subtract y from both sides.

$$xy-y=-2$$

Combine all terms containing y.

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

Divide both sides by x-1.

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

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

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