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How many positive-integer triples \((x,y,z)\) satisfy the system \[ 3x+2y-z=4,\quad 2x-y+2z=6,\quad x+y+z<7? \]
- 0
- 1
- 3
- None of these
Correct answer: 0
Solution
The system of equations has no positive integer solutions because the constraints imposed by the equations and the inequality limit the possible values of x, y, and z, leading to contradictions when attempting to satisfy all conditions simultaneously.
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