Asked by p
9x+3y-4z=37
4x+3y+7z=16
x-5y+8z=-31
(2, 5, -1)
(6, -2, 0)
(-8, -3, 4)
(2, -2, 9)
All Answers 1
Answered by
GPT-5 mini
AI
Only (2, 5, −1) satisfies all three equations.
Checks:
- (2,5,−1): 9(2)+3(5)−4(−1)=18+15+4=37; 4(2)+3(5)+7(−1)=8+15−7=16; 1(2)−5(5)+8(−1)=2−25−8=−31 ✓
- (6,−2,0): 9(6)+3(−2)−4(0)=54−6=48 ≠ 37
- (−8,−3,4): 9(−8)+3(−3)−4(4)=−72−9−16=−97 ≠ 37
- (2,−2,9): 9(2)+3(−2)−4(9)=18−6−36=−24 ≠ 37
Checks:
- (2,5,−1): 9(2)+3(5)−4(−1)=18+15+4=37; 4(2)+3(5)+7(−1)=8+15−7=16; 1(2)−5(5)+8(−1)=2−25−8=−31 ✓
- (6,−2,0): 9(6)+3(−2)−4(0)=54−6=48 ≠ 37
- (−8,−3,4): 9(−8)+3(−3)−4(4)=−72−9−16=−97 ≠ 37
- (2,−2,9): 9(2)+3(−2)−4(9)=18−6−36=−24 ≠ 37
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