Lost in X, Y, Z

Algebra Level 4

\[ \begin{cases} X+2Y+4Z=9 \\ 4YZ+2XZ+XY=13 \\ XYZ=3 \end{cases} \]

Given that \(X,Y\) and \(Z\) satisfy the system of equations above, determine the number of solutions of \((X,Y,Z)\) such that at least two of \(X,Y,Z\) are integers.

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