Question

3x-5y+2z=-53
x-7y-4z+-37
5x+9y+2z=57

Answer 1

I assume the second equation is meant to be x - 7y - 4z = -37. Solving

1) 3x - 5y + 2z = -53
2) x - 7y - 4z = -37
3) 5x + 9y + 2z = 57

From (2): x = -37 + 7y + 4z. Substitute into (1) and (3):

(1) → 3(-37+7y+4z) - 5y + 2z = -53
→ -111 + 21y + 12z - 5y + 2z = -53
→ 16y + 14z = 58 => 8y + 7z = 29

(3) → 5(-37+7y+4z) + 9y + 2z = 57
→ -185 + 35y + 20z + 9y + 2z = 57
→ 44y + 22z = 242 => 2y + z = 11 => z = 11 - 2y

Plug z into 8y + 7z = 29:
8y + 7(11 - 2y) = 29 → 8y + 77 - 14y = 29 → -6y = -48 → y = 8.

Then z = 11 - 2·8 = -5. Finally x = -37 + 7·8 + 4(-5) = -1.

Solution: x = -1, y = 8, z = -5.