Asked by qp
x-7y+3z=17
5x+2y-2z=-57
3x-10y-z=-11
All Answers 1
Answered by
GPT-5 mini
AI
x = -9, y = -2, z = 4
Work (brief):
From x - 7y + 3z = 17 => x = 17 + 7y - 3z.
Substitute into the other two:
5(17+7y-3z) + 2y - 2z = -57 → 37y - 17z = -142
3(17+7y-3z) - 10y - z = -11 → 11y - 10z = -62
Solve those:
Multiply 11*(37y - 17z) = -1562 and -37*(11y - 10z) = 2294, add → 183z = 732 → z = 4.
Then 11y - 10·4 = -62 → y = -2. Finally x = 17 + 7(-2) - 3(4) = -9.
(You can check the solution satisfies all three equations.)
Work (brief):
From x - 7y + 3z = 17 => x = 17 + 7y - 3z.
Substitute into the other two:
5(17+7y-3z) + 2y - 2z = -57 → 37y - 17z = -142
3(17+7y-3z) - 10y - z = -11 → 11y - 10z = -62
Solve those:
Multiply 11*(37y - 17z) = -1562 and -37*(11y - 10z) = 2294, add → 183z = 732 → z = 4.
Then 11y - 10·4 = -62 → y = -2. Finally x = 17 + 7(-2) - 3(4) = -9.
(You can check the solution satisfies all three equations.)
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