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misal

1/x = a  maka x = 1/a

1/y = b maka y = 1/b

1/z = c maka z = 1/c

1/x+3/y+6/z=2 ⇒ a + 3b + 6c = 2... (i)

3/x+8/y-4/z=3 ⇒ 3a + 8b- 4c = 3... (ii)

1/x-6/y-8/z= -2 ⇒ a - 6b -8c = - 2. ..(iii)

eliminasi a (i) dan (ii)

a + 3b + 6c = 2 . . . (x 3)

3a + 8b- 4c = 3

3a + 9b + 18 c = 6

3a + 8b - 4c = 3   -

b + 22c = 3 . .. (iv)

eliminasi a (i) dan (iii)

a + 3b + 6c = 2

a - 6b -8c = - 2    -

9b + 14c = 4 . .. (v)

eliminasi b (iv) dan (v)

b + 22 c = 3. .. (x 9)

9b +14c = 4

9b + 198 c= 27

9b +  14c = 4   -

184 c =  23

c =  23/184= 1/8

subsitusi c = 1/8 , ke (iv)

b + 22 c = 3

b + 22(1/8) = 3

b  + 22/8 = 3

b =  3 - 22/8 = 1/4

substitusi  b = 1/4 dan  c = 1/8 ke (i)

a + 3b + 6c = 2

a + 3(1/4) + 6(1/8) = 2

a +  3/4 + 6/8 = 2

a + 3/2 = 2

a = 2 - 3/2

a =  1/2

maka nilai  

x = 1/a = 2

y = 1/b = 4

z = 1/c =  8