Question

2x-6y+9z=-8
5x+y+2z=10
3x+y-8z=-28
(2, -2, 9)


(-1, 7, 4)


(8, -2, -5)


(-7, 0, -3)

Answer 1

Only (-1, 7, 4) is a solution.

Check each:

(2, -2, 9)
- Eq1: 2(2) - 6(-2) + 9(9) = 4 + 12 + 81 = 97 ≠ -8 → not a solution.

(-1, 7, 4)
- Eq1: 2(-1) - 6(7) + 9(4) = -2 - 42 + 36 = -8
- Eq2: 5(-1) + 7 + 2(4) = -5 + 7 + 8 = 10
- Eq3: 3(-1) + 7 - 8(4) = -3 + 7 - 32 = -28
All three hold, so this is a solution.

(8, -2, -5)
- Eq1: 2(8) - 6(-2) + 9(-5) = 16 + 12 - 45 = -17 ≠ -8 → not a solution.

(-7, 0, -3)
- Eq1: 2(-7) - 6(0) + 9(-3) = -14 + 0 - 27 = -41 ≠ -8 → not a solution.