F. 2 Method of Elimination

(1/x) + (2/y) = (5/6) ...... (i)
‎(2/x) - (3/y) = (2/3) ...... (ii)

Let a = (1/x), b = (1/y).

From (i):
a + 2b = (5/6) ...... (iii)

From (ii):
2a - 3b = (2/3) ...... (iv)

(iii)*2:
2a + 4b = (5/3) ...... (v)

(v) - (vi)
7b = 1
b = 1/7
Then y = 7

Put b = (1/7) into (iii):
a + 2(1/7) = (5/6)
a = (35/42) - (12/42)
a = 23/42
Then x = 42/23

Ans: x = 42/23 and y = 7