Find all ordered triples (x,y,z) of real numbers which satisfy the following system of equations:
\left\{\begin{array}{rcl} xy & \equal{} & z \minus{} x \minus{} y \\
xz & \equal{} & y \minus{} x \minus{} z \\
yz & \equal{} & x \minus{} y \minus{} z \end{array} \right.
algebrasystem of equations