Question

4x+y-3z=45
6x-4y+3z=41
2x-7y-11z=85
(-7, 0, -3)


(2, -2, 9)


(8, -2, -5)


(-1, 7, 4)

Answer 1

Check each point by substituting (x,y,z) into the three equations.

For (-7,0,-3):
Eq1: 4(-7)+0-3(-3) = -28+9 = -19 ≠ 45 → not a solution.

For (2,-2,9):
Eq1: 4(2)+(-2)-3(9) = 8-2-27 = -21 ≠ 45 → not a solution.

For (8,-2,-5):
Eq1: 4(8)+(-2)-3(-5) = 32-2+15 = 45
Eq2: 6(8)-4(-2)+3(-5) = 48+8-15 = 41
Eq3: 2(8)-7(-2)-11(-5) = 16+14+55 = 85
All three hold → (8,-2,-5) is a solution.

For (-1,7,4):
Eq1: 4(-1)+7-3(4) = -4+7-12 = -9 ≠ 45 → not a solution.

Answer: only (8, -2, -5) satisfies the system.