Determine all triples $(x, y,z)$ consisting of three distinct real numbers, that satisfy the following system of equations:
 $\begin {cases}x^2 + y^2 = -x + 3y + z \\
y^2 + z^2 = x + 3y - z \\
x^2 + z^2 = 2x + 2y - z \end {cases}$