Selesaikan himpunan penyelesaian persamaan berikut 1. 4x+2y+z = 6 2x+3y-z =6,5 3x+2y+2z = 7 2. 3x+2y+z=12 4x+3y+2z=17 x+y+3z=5 tolong jawab dengan cara

SPLTV

Nomor 1:
4x + 2y + z = 6 → pers.1
2x + 3y - z = 6,5 → pers.2
3x + 2y + 2z = 7 → pers.3

Eliminasi pers.1 dan 2
4x + 2y + z = 6
2x + 3y - z = 6,5
____________+
6x + 5y = 12,5 → pers.4

Eliminasi pers. 1 dan 3
4x + 2y + z = 6
3x + 2y + 2z = 7
Pers.1 dikali 2
8x + 4y + 2z = 12
3x + 2y + 2z = 7
_____________-
5x + 2y = 5 → pers.5

Eliminasi pers.4 dan 5
6x + 5y = 12,5
5x + 2y = 5
Pers.4 dikali 2 dan pers.5 dikali 5
12x + 10y = 25
25x + 10y = 25
___________-
-13x = 0
x = 13

Substitusikan nilai x ke pers.5
5x + 2y = 5
65 + 2y = 5
2y = 5 - 65
2y = -60
y = -30

Substitusikan nilai x dan y ke pers.1
4x + 2y + z = 6
52 - 60 + z = 6
-8 + z = 6
z = 14

HP = {(13, -30, 14)}

Nomor 2:
3x + 2y + z = 12 → pers.1
4x + 3y + 2z = 17 → pers.2
x + y + 3z = 5 → pers.3

Eliminasi pers.1 dan 2
3x + 2y + z = 12
4x + 3y + 2z = 17
Pers.1 dikali 2
6x + 4y + 2z = 24
4x + 3y + 2z = 17
_____________-
2x - y = 7 → pers.4

Eliminasi pers.1 dan 3
3x + 2y + z = 12
x + y + 3z = 5
Pers.1 dikali 3
9x + 6y + 3z = 36
x + y + 3z = 5
_____________-
8x - 5y = 31 → pers.5

Eliminasi pers.4 dan 5
2x - y = 7
8x - 5y = 31
Pers.1 dikali 4
8x - 4y = 28
8x - 5y = 31
_________-
y = -3

Substitusikan nilai y ke pers.4
2x - y = 7
2x + 3 = 7
2x = 4
x = 2

Substitusikan nilai x dan y ke pers.1
3x + 2y + z = 12
6 - 6 + z = 12
z = 12

HP = {(2, -3, 12)}