diketahui x,y dan z memenuhi sistem persamaan: 1/x - 1/y + 2/z =9.....(1) 2/x + 1/y - 3/z=-9....(2) 4/x - 2/y + 1/z=2....(3) Nilai x - y + z=.... A. 1/12 B. 1/6

Misal 1/x = p, 1/y = q dan 1/z = r

p - q + 2r = 9 ..... ....... (1)
2p + q - 3r = -19 ........ (2)
4p - 2q + r = 2 .... ..... (3)

(1) dan (2) dieliminasi
p - q + 2r = 9
2p + q - 3r = -19
---------------------- +
3p - r = -10 ..................... (4)

(1) dan (3) dieliminasi
p - q + 2r = 9 ..|x2| 2p - 2q + 4r = 18
4p - 2q + r = 2 | x1| 4p - 2q + r = 2
------------------------------------------------- -
.................................. -2p + 3r = 16 ......... (5)

4) dan (5) =pdieliminasi
3p - r = -10 .... |x3| 9p - 3r = -30
-2p + 3r = 16 ..|x1| -2p + 3r = 16
------------------------------------------ +
...................................7p = -14 => p = -2

substitusikan p = -2 ke pers (4) :
3p - r = -10
=> 3(-2) - r = -10
=> -r = -4 => r = 4

substitusikan p = -2 dan r = 4 ke pers (1) :
p - q + 2r = 9
=> -2 - q + 2(4) = 9
=> 6 - q = 9
=> q = -3

p = 1/x = -2 => x = -1/2
q = 1/y = -3 => y = -1/3
r = 1/z = 4 => z = 1/4
x - y + z = -1/2 - (-1/3) + 1/4 = (-6 + 4 + 3)/12 = 1/12