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How many positive-integer triples (x,y,z) satisfy the system 3x+2y-z=4, 2x-y+2z=6, x+y+z<7?

1. 0
2. 1
3. 3
4. None of these

Correct answer: 1

Solution

From z=3x+2y-4 substituted into 2x-y+2z=6 gives 8x+3y=14. Positive integers: x=1,y=2,z=3 (x+y+z=6<7). x>=2 gives 8x>14, impossible. So exactly 1 triple.

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