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