Answer:
Step-by-step explanation:
3x – y + 2z = 6 - - - - - - - - - 1
-x + y = 2 - - - - - - - - - - - - -2
x – 2z = -5 - - - - - - - - - - - -3
From equation 2, x = y - 2
From equation 3, x = 2z - 5
Substituting x = y - 2 and x = 2z - 5 into equation 1, it becomes
3(y - 2) – y + 2z = 6
3y - 6 - y + 2z = 6
3y - y + 2z = 6 + 6
2y + 2z = 12 - - - - - - - - - 4
3(2z - 5) – y + 2z = 6
6z - 15 - y + 2z = 6
- y + 6z + 2z = 6 + 15
- y + 8z = 21 - - - - - - - - - - 5
Multiplying equation 4 by 1 and equation 5 by 2, it becomes
2y + 2z = 12
- 2y + 16z = 42
Adding both equations
18z = 54
z = 54/18 = 3
Substituting z = 3 into equation 5, it becomes
- y + 8×3 = 21
- y + 24 = 21
- y = 21 - 24 = - 3
y = 3
Substituting y = 3 into equation 2, it becomes
-x + 3 = 2
- x = 2 - 3 = -1
x = 1
