# 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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