Solve the system.
A) (4, 4, -5)
B) (4, -3, -5)
C) (6, -3, -5)
D) The system is inconsistent
E) The system is dependent

Question

Solve the system. 
A) (4, 4, -5) 
B) (4, -3, -5) 
C) (6, -3, -5) 
D) The system is inconsistent 
E) The system is dependent

Quizplus · Accepted Answer

1. Add equation 1 and equation 2 to eliminate x: 
    x + y - 2z = 0 
    y - z = 9 
2. Add equation 2 and equation 3 to eliminate y: 
    x - z = -1 
    -x - 2z = -9 
3. Solve for z from equation 2: 
    z = (x + 9)/2 
4. Substitute z into equation 1: 
    x + y - (x + 9) = 0 
    y = -9 
5. Substitute z and y into equation 3: 
    x + 2(x + 9)/2 = 5 
    x + x + 9 = 5 
    x = -2 
6. Therefore, the solution is (x, y, z) = (-2, -9, 3) which matches choice B.

Solve the System