Question

10x+7y-2z=46
3x-2y+9z=22
5x+y-3z=28
(6, -2, 0)


(-8, 3, 4)


(5, -2, 3)


(2, 5, -1)

Answer 1

Only (6, -2, 0) satisfies all three equations.

Checks:
- (6, -2, 0):
10(6)+7(-2)-2(0)=60-14=46
3(6)-2(-2)+9(0)=18+4=22
5(6)+(-2)-3(0)=30-2=28
→ satisfies all three.

- (-8, 3, 4):
10(-8)+7(3)-2(4) = -80+21-8 = -67 ≠ 46

- (5, -2, 3):
10(5)+7(-2)-2(3) = 50-14-6 = 30 ≠ 46

- (2, 5, -1):
10(2)+7(5)-2(-1) = 20+35+2 = 57 ≠ 46

So the solution is (6, -2, 0).