diketahui spltv= x+4y-z=1 2x+6y+z=-8 -x+2y+z=2 tentkan nilai x*-y*+z*

Materi : SPLTV
Kelas : X SMA

x + 4y - z = 1 ............. 1)
2x + 6y + z = -8 ....... 2)
-x + 2y + z = 2 .......... 3)


Eliminasi Nilai x pada persamaan 1 dan 3 :
x + 4y - z = 1
-x + 2y + z = 2
◆◆◆◆◆◆◆◆◆◆◆ [+]
6y = 3
y = 3/6
y = 1/2

Eliminasi nilai x pada persamaan 1 dan 2 :
x + 4y - z = 1 ........... ×2
2x + 6y + z = -8 ..... ×1
◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆
2x + 8y - 2z = 2
2x + 6y + z = -8
◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆ [-]
2y - 3z = 10 ......... 4)

Substitusi nilai y ke pers 5 :
2y - 3z = 10
2(1/2) - 3z = 10
1 - 3z = 10
-3z = 10 - 1
-3z = 9
z = -3

Substitusi nilai y dan z ke persamaan 1 :
x + 4y - z = 1
x + 4(-3) - 1/2 = 1
x - 12 - 1/2 = 1
x = 1 + 12 + 1/2
x = 13 + 1/2
x = 26/2 + 1/2
x = 27/2
x = 13,5

Hp = { 27/2 , 1/2 , -3 }