3/x - 4/y + 6/z = 1
9/x + 8/y - 12/z = 3
9/x - 4/y + 12/z = 4
misalkan..
1/x = a
1/y = b
1/z = c
3a - 4b + 6c = 1 (persamaan 1)
9a + 8b - 12c = 3 (persamaan 2)
9a - 4b + 12c = 4 (persamaan 3)
eliminasi persamaan 2 dan 3
9a + 8b - 12c = 3
9a - 4b + 12c = 4
------------------------- -
12b - 24c = -1 (persamaan 4)
eliminasi persamaan 1 dan 2
3a - 4b + 6c = 1 (x3) 9a - 12b + 18c = 3
9a + 8b - 12c = 3 (x1) 9a + 8b - 12c = 3
------------------------- -
-20b + 30c = 0
20b = 30c
b = 3c/2 (persamaan 5)
subsitusikan b ke persamaan 4
12b - 24c = -1
12(3c/2) - 24c = -1
6(3c) - 24c = -1
18c - 24c = -1
-6c = -1
6c = 1
c = 1/6
subsitusikan c ke persamaan 5
b = 3c/2
b = 3(1/6) / 2
b = (1/2) / 2
b = 1/4
subsitusikan b, c ke persamaan 1
3a - 4b + 6c = 1
3a - 4(1/4) + 6(1/6) = 1
3a - 1 + 1 = 1
3a = 1
a = 1/3
lalu, cari nilai x, y, dan z nya..
1/x = a
1/x = 1/3
x = 3
1/y = b
1/y = 1/4
b = 4
1/z = 1/c
1/z = 1/6
z = 6
maka, x = 3, b = 4, z = 6
[answer.2.content]
