1/x+4/y+3/z=8. 3/x-1/y+1/z=3. 2/x-3/y+1/z=0. tentukan x,y dan z

jawab
misalkan
a  = 1/x
b = 1/y
c = 1/z

(i) 1/x + 4/y + 3/z = 8 → a + 4b + 3c = 8
(ii) 3/x - 1/y + 1/z = 3 →  3a - b + c  = 3
(iii)  2/x - 3/y+ 1/z = 0 → 2a - 3b + c = 0

dari (i dan  ii)
a + 4b + 3c = 8
3a - b + c = 3.....}kalikan 3

a + 4b + 3c = 8
9a - 3b + 3c = 9....||(-)
-8a  + 7b  = - 1 ....(iv)


(ii) dan (iii)
3a - b + c = 3.
2a - 3b + c = 0 ...||(-)
a + 2b = 3 ...(v)

dari iv dan v
-8a + 7b = -1
a  + 2b = 3 ...{kali 8

-8a + 7b = - 1
8a + 16b = 24...||(+)
23b = 23
b = 1
a + 2b = 3
a + 2(1) =3
a = 1

a+ 4b + 3c = 8
1 + 4 + 3c = 8
3c= 3
c = 1

a= 1 → x = 1
b = 1 → y = 1
c = 1 → z = 1