Dik spltv 2×-y+z=12 X+2y+z=5 3x-y+2z=19 Himpunan penyelesaian SPLTV tersebut adalah

eliminasi baris 1 dan 2

2x + (-y) + z = 12 2x - y + z = 12
x + 2y + z = 5 2x + 4y +2z = 10 _
-5y - z = 2 ( a )

eliminasi baris 2 dan 3

x + 2y + z = 5 3x + 6y + 3z = 15
3x - y + 2z = 19 3x - y + 2z = 19 _
7y + z = -4 ( b )

eliminasi (a) dan (b)

-5y - z = 2 5y + z = 2
7y + z = -4 7y + z = -4 _
-2y = 6
y = -3

subsitusikan

7y + z = -4
7(-3) + z = -4
-21 + z = -4
z = -4 + 21
z = 17

x + 2y + z = 5
x + 2(-3) + 17 = 5
x -6 + 17 = 5
x + 11 = 5
x = 5 -11
x = -6

hp : {x,y,z}
hp : { -6 , -3 , 17 }