SE-SKOLORNAS 1977 Problem 3

Show that the only integral solution to $$\left\{ \begin{array}{l} xy + yz + zx = 3n^2 - 1 x + y + z = 3n \end{array} \right.$$ with $x \geq y \geq z$ is $x=n+1$ , $y=n$ , $z=n-1$ .