An algebra problem by Aira Thalca

Algebra Level 5

\[\begin{cases} x+2y+4z=9 \\ 4yz+2xz+xy=13\\ xyz=3\end{cases} \]

Find the number of solutions \((x, y, z)\) to the system of equations above such that at least two of \(x, y, z\) are integers.

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