Solve z-1-x=y-1+xy

$$z-1-x=y-1+xy$$

Solve for x

$$\left\{\begin{matrix}x=\frac{z-y}{y+1}\text{, }&y\neq -1\\x\in \mathrm{R}\text{, }&z=-1\text{ and }y=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract xy from both sides.

$$z-1-x-xy=y-1$$

Subtract z from both sides.

$$-1-x-xy=y-1-z$$

Add 1 to both sides.

$$-x-xy=y-1-z+1$$

Add -1 and 1 to get 0.

$$-x-xy=y-z$$

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by -y-1.

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

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

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

Divide y-z by -y-1.

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

Solve for y

$$\left\{\begin{matrix}y=-\frac{x-z}{x+1}\text{, }&x\neq -1\\y\in \mathrm{R}\text{, }&z=-1\text{ and }x=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$y-1+xy=z-1-x$$

Add 1 to both sides.

$$y+xy=z-1-x+1$$

Add -1 and 1 to get 0.

$$y+xy=z-x$$

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by 1+x.

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

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

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