himpunan penyelesaian dari 1/x+2/y+4/z=1, -1/x+4/y+12/z=0, 2/x+8/y+4/z=-1

jawab
misal 
1/x = a
1/y = b
1/z = c

1/x + 2/y + 4/z = 1 → a + 2b + 4c = 1 ..(i)
-1/x + 4/y + 12/z = 0 → -a + 4b + 12c =0 ..(ii)
2/x + 8/y + 4z = -1 → 2a + 8b + 4c = - 1 ...(iii)

(i) dan (ii)
a + 2b + 4c = 1
-a + 4b + 12c = 0  ||(+)
6b + 16 c = 1 ..(iv)

(ii) dan (iii)
-a + 4b +12c = 0 ..}kali 2
2a + 8b + 4c = -1

-2a + 8b + 24c  = 0
2a + 8b  - 4c = - 1...||(+)
16 b + 20 c = -1 ...(v)

dari (iv) dan (v)
6b + 16c = -1..} kali 8
16b + 20c = -1} kali 3

48b + 128 c = -8
48b + 60 c = - 3..||-()
68 c= -5
c =-5/68

48b + 60 c = - 3
48 b + 60(- 5/68)= - 3
48 b = - 3 + 300/68
b = 96/68  x 1/48
b = 1/34

a + 2b + 4c = 1
a + 2(1/34) + 4(-5/68) = 1
a + 1/17 - 20/68 = 1
a = 21/17

a = 21/17 → x = 17/21
b = 1/34  → y = 34
c = -5/68  → z = - 68/5