Question

9x+3y-4z=37
4x+3y+7z=16
x-5y+8z=-31

Answer 1

Solve by elimination.

Subtract (1) from (2):
(4x+3y+7z) - (9x+3y-4z) = 16 - 37
=> -5x + 11z = -21. (A)

Eliminate y between (1) and (3): 5*(1) + 3*(3)
5(9x+3y-4z) + 3(x-5y+8z) = 5*37 + 3*(-31)
=> 45x+15y-20z + 3x-15y+24z = 185 - 93
=> 48x + 4z = 92
=> 12x + z = 23. (B)

From (B): z = 23 - 12x. Substitute in (A):
-5x + 11(23 - 12x) = -21
=> -5x + 253 -132x = -21
=> -137x = -274
=> x = 2.

Then z = 23 - 12(2) = -1. Use (2) to get y:
4(2) + 3y + 7(-1) = 16 => 8 + 3y -7 = 16 => 3y = 15 => y = 5.

Solution: x = 2, y = 5, z = -1.