Cari Himpunan Penyelsaiannya 1) 2/p + 2/q - 3/r = 11 6/p - 9/q - 2/r = -1 2/p - 4/q + 18/r = -19

Bab Persamaan Linear 3 Variabel
Matematika SMA Kelas X

1/p = a
1/q = b
1/r = c

2a + 2b - 3c = 11 → persamaan 1
2a - 4b + 18c = -19 → persamaan 3
---------------------------- -
6b - 21c = 30 → persamaan 4
2b - 7c = 10

2a + 2b - 3c = 11 → persamaan 1
↓ dikalikan 3 ↓
6a + 6b - 9c = 33 → persamaan 2
6a - 9b - 2c = -1
--------------------------- -
15b - 7c = 34 → persamaan 5

persamaan 4 dan 5

15b - 7c = 34
..2b - 7c = 10
--------------------- -
13b = 24
b = 24/13

2b - 7c = 10
2 . 24/13 - 7c = 10
7c = 48/13 - 130/13
c = -82/(7 . 13)
c = -82/91

2a + 3b - c = 11
2a + 3 . 24/13 - (-82/91) = 11
2a = 1.001/91 - (72 . 7 + 82)/91
2a = (1.001 - 586)/91
a = 415/(2 . 91)
a = 415/182

p = 1/a
p = 182/415

q = 1/b
q = 13/24

r = 1/c
r = -91/82

HP = {(182/415, 13/24, -91/82)}

persamaan satu dgn dua
2/p + 2/q - 3/r = 11 ------ (×3)
6/p + 9/q - 2/r = -1 ------ (×1)

6/p + 6/q - 9/r = 33
6/p + 9/q - 2/r = -1
_______________-
-3/q - 7/r = 34

persamaan satu dgn tiga
2/p + 2/q - 3/r = 11
2/p - 4/q + 18/r = -19
_______________-
6/q - 21/r = 30

persamaan dua dgn tiga
-3/q - 7/r = 34 ----- (×2)
6/q - 21/r = 30 ---- (×1)

-6/q - 14/r = 68
6/q - 21/r = 30
____________+
-35/r = 98
r = - 35/98
r = - 5/14

6/q - 21/r = 30
2/q - 7/r = 15
2/q - 7/(- 5/14) = 15
2/q + 98/5 = 15
2/q = 75/5 - 98/5
2/q = - 23/5
q = 2 × - 5/23
q = - 10/23

2/p + 2/q - 3/r = 11
2/p + 2/(-10/23) - 3/(-5/14) = 11
2/p - 46/10 + 42/5 = 11
2/p = 11 + 46/10 - 42/5
2/p = (110 + 46 - 84) / 10
2/p = 72/10
p = 2 × 10/72
p = 10/36
p = 5/18

HP {p , q , r}
HP {5/18 , -10/23 , -5/14}

semoga berguna +_+