Penjelasan dengan langkah-langkah:

x - 2y + z = 6 (1)

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

7x - 6y - z = 10 (3)

Eliminasi variabel z pd pers. 1 dan 2

x - 2y + z = 6 (×2)

3x + y - 2z = 4 (×1)

2x - 4y + 2z = 12

3x + y - 2z = 4

____________(+)

5x - 3y = 16 (4)

Eliminasi variabel z pd pers. 1 dan 3

x - 2y + z = 6

7x - 6y - z = 10

____________(+)

8x - 8y = 16 (5)

Eliminasi variabel y pd pers. 4 dan 5

5x - 3y = 16 (×8)

8x - 8y = 16 (×3)

40x - 24y = 128

24x - 24y = 48

____________(-)

16x = 80

x = 80/16

x = 5

Substitusi nilai x ke pers. 4

5(5) - 3y = 16

25 - 3y = 16

-3y = 16 - 25

-3y = -9

y = -9/-3

y = 9/3

y = 3

Substitusi nilai x dan y ke pers. 1

x - 2y + z = 6

5 - 2(3) + z = 6

5 - 6 + z = 6

-1 + z = 6

z = 6 + 1

z = 7

HP = {5, 3, 7}