Can you find the solution?

Algebra Level 5

The number of solutions (x, y, z) to the system of equations \[x+2y+4z=9\] \[4yz+2xz+xy=13\] \[xyz=3\] such that at least two of x, y, z are integers is \[Note-\:\:Its\:\:an\:\:old\:\:KVPY\:\:question\]

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