5/x+9/y=6, 1/x+5/y=3 then what is the value of 1/x+1/y
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Let 1/x be 'a' and 1/y be 'b'
5/x + 9/y = 6
5a + 9b = 6 ------> (1)
1/x + 5/y = 3
a + 5b = 4 -------> (2)
(2) × 5:
5(a + 5b) = 4 × 5
5a + 25b = 20 ------> (3)
(3) - (1):
16b = 14
b = 14/16
b = 7/8
Substituting b in (2):
a + 5(7/8) = 4
a = 4 - 35/8
a = (32-35)/8
a = 3/8
Therefore,
1/x + 1/y = 3/8 + 7/8
= 10/8
= 5/4
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