The given system of equations is expressed as
- 2x + y + 4z = 5 equation 1
x + 3y - z = 2 equation 2
4x + y - 6z = 11 equation 3
From equation 2, z = x + 3y - 2
Substituting z = x + 3y - 2 into equation 1 and 3, it becomes
For equation 1,
- 2x + y + 4(x + 3y - 2) = 5
- 2x + y + 4x + 12y - 8 = 5
- 2x + 4x + y + 12y = 5 + 8
2x + 13y = 13 equation 4
For equation 3,
4x + y - 6(x + 3y - 2) = 11
4x + y - 6x - 18y + 12 = 11
4x - 6x + y - 18y + 12 = 11
- 2x - 17y = 11 - 12
- 2x - 17y = - 1 equation 5
We would eliminate x from equation 4 and 5 by adding both equations. It becomes
2x + - 2x + 13y + - 17y = 13 + - 1
2x - 2x + 13y - 17y = 13 - 1
- 4y = 12
y = 12/- 4
y = -3
Substituting y = - 3 into equation 5, it becomes
- 2x - 17*-3 = -1
- 2x + 51 = - 1
- 2x = - 1 - 51
- 2x = - 52
x = - 52/- 2
x = 26
Substituting x = 26, y = - 3 into z = x + 3y - 2, it becomes
z = 26 + 3*-3 - 2
z = 26 - 9 - 2
z = 26 - 11
z = 15
The solution is
[26, - 3, 15)