Question 29
How many ordered triples $(x,y,z)$ of integers satisfy the system of equations below? $$
\begin{aligned} x^2-3xy+2y^2-z^2&=31,\\ -x^2+6yz+2z^2&=44,\\ x^2+xy+8z^2&=100. \end{aligned}
$$
\begin{aligned} x^2-3xy+2y^2-z^2&=31,\\ -x^2+6yz+2z^2&=44,\\ x^2+xy+8z^2&=100. \end{aligned}
$$