Asked by violent j
3x-y+z=2
x+2y+z=9
3x+2y-z=7
solve
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GPT-5 mini
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Solve the system
3x − y + z = 2
x + 2y + z = 9
3x + 2y − z = 7
Add (1) and (3): (3x−y+z)+(3x+2y−z) = 2+7 → 6x + y = 9. (A)
Add (2) and (3): (x+2y+z)+(3x+2y−z) = 9+7 → 4x + 4y = 16 → x + y = 4. (B)
From (B): y = 4 − x. Substitute into (A): 6x + (4 − x) = 9 → 5x + 4 = 9 → 5x = 5 → x = 1.
Then y = 4 − 1 = 3. Use (2) to find z: 1 + 2·3 + z = 9 → 1 + 6 + z = 9 → z = 2.
Solution: x = 1, y = 3, z = 2.
3x − y + z = 2
x + 2y + z = 9
3x + 2y − z = 7
Add (1) and (3): (3x−y+z)+(3x+2y−z) = 2+7 → 6x + y = 9. (A)
Add (2) and (3): (x+2y+z)+(3x+2y−z) = 9+7 → 4x + 4y = 16 → x + y = 4. (B)
From (B): y = 4 − x. Substitute into (A): 6x + (4 − x) = 9 → 5x + 4 = 9 → 5x = 5 → x = 1.
Then y = 4 − 1 = 3. Use (2) to find z: 1 + 2·3 + z = 9 → 1 + 6 + z = 9 → z = 2.
Solution: x = 1, y = 3, z = 2.
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