Linier 3 variable. 2x+y-z=5 x-y+z=-2 3x+2y+4z=3

2x + y - z = 5
x -y + z = -2
---------------+
3x = 3
x = 1

1 -y + z = -2 3 + 2y + 4z = 3
-y + z = -3 ( x 4) 2y + 4z = 0

2y + 4z = 0
-4y + 4z = -12
-------------- -
6y = 12
y = 2
x-y+z = -2
1-2 + z = -2
-1 + z = -2
z = -1

eliminasi pers (1) dan (2)
2x +y-z = 5
 x -y+z=-2
3x      = 3
        x= 3: 3
        x= 1

eliminasi pers (1) dan (3)
2x + y - z = 5-------------> dikali 2
3x +2y+4z= 3-------------> dikali 1
maka :
4x + 2y - 2z = 10
3x + 2y + 4z= 3
  x         -6z = 7...........(*)

eliminasi pers (2) dan (3)
x - y + z  = -2---------------> dikali 2
3x+2y+4z= 3----------------> dikali 1
maka :
2x - 2y + 2z = -2
3x + 2y+ 4z = 3
5x        + 6z = 1................(**)

substitusi x = 1 ke pers (*)
1 - 6z = 7
    -6z = 6
       z = -1

substitusi x=1, z=-1 ke pers (1)
2x + y - z =5
2(1)+y-(-1)= 5
2 + y + 1 = 5
3 + y = 5
      y = 2

Maka HP = {1, 2, -1}