Solve x+y+xy=1

$$x + y + x y = 1$$

Solve for x

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

$$y\neq -1$$

Steps for Solving Linear Equation

Subtract y from both sides.

$$x+xy=1-y$$

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by 1+y.

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

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

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

Solve for y

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

$$x\neq -1$$

Steps for Solving Linear Equation

Subtract x from both sides.

$$y+xy=1-x$$

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by 1+x.

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

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

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