Let 1/x be a and 1/y be b. a/2 + b/3 = 2 and a/3 + b/2 = 13/6. Now take LCM. 3a/6 + 2b/6 = 2 and 2a/6 + 3b/6 = 13/6. Send the denominator to RHS. 3a + 2b = 12 and 2a + 3b = 13. Multiplying eq 1 by 2 and eq 2 by 1 . We get 6a + 4b = 24 and 6a + 9b = 39. Now you can eliminate.

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