2/x+1/y=2 4/y+3/z=5 3/x+2/3=3 nilai 1/x+/1y+1/y=

Misal 1/x = a, 1/y = b, 1/z = c

Persamaan menjadi
2a + b = 2 (i)
4b + 3c = 5 (ii)
3a + 2c = 3 (iii)

Eliminasi i dan ii

2a + b = 2 |x 4|
=>8a + 4b = 8
=>4b + 3c = 5
--------------------- (-)
8a - 3c = 3 (iv)

Eliminasi iv dan iii
8a - 3c = 3 |x 2|
3a + 2c = 3|x 3|

16a - 6c = 6
9a + 6c = 9
--------------- (+)
25a = 15
a = 15/25
a = 3/5

3a + 2c = 3
3(3/5) + 2c = 3
2c = 3 - 15/3
c = 6/5 : 2
c = 3/5

2a + b = 2
2(3/5) + b = 2
b = 2 - 6/5
b = 4/5

1/x + 1/y + 1/z
=>a + b + c
=>3/5 + 4/5 + 3/5
=>10/5
=>2