Answer:x = 0, y = 3, z = 2
Step-by-step explanation:
The given system of equations is expressed as
x - y + 4z = 5 - - - - - - - - - - - - - -1
4x + z = 2
z = 2 - 4x- - - - - - - - - - - - - -2
x + 5y + z = 17- - - - - - - - - - - - - -3
From equation
Substituting equation 2 into equation 1 and equation 3, it becomes
x - y + 4(2 - 4x) = 5
x - y + 8 - 16x = 5
x - 16x - y = 5 - 8
- 15x - y = - 3 - - - - - - - - - - - - - -4
x + 5y + 2 - 4x = 17
x - 4x + 5y = 17 - 2
- 3x + 5y = 15- - - - - - - - - - - - - -5
We would eliminate y by multiplying equation 4 by 5 and equation 5 by 1. It becomes
- 1
- 75x - 5y = - 15
- 3x + 5y = 15
Adding both equations, it becomes
- 78x = 0
x = 0
Substituting x = 0 into equation 2, it becomes
z = 2 - 4 × 0
z = 2
Substituting x = 0 and z = 2 into equation 1, it becomes
0 - y + 4 × 2 = 5
- y + 8 = 5
y = 8 - 5
y = 3
