5/(x-1) + 1/(y-2) = 26/(x-1) – 3/(y-2) = 1

Solution: Substituting 1/(x-1) = m and 1/(y-2) = n in the given equations, we get, 5m + n = 2 …………………………(i) 6m – 3n = 1 ……………………….(ii) Multiplying equation (i) by 3, we get 15m + 3n = 6 …………………….(iii) Adding (ii) and (iii) we get 21m = 7 m = 1/3 Putting this value in equation (i), we get 5×1/3 + n = 2 n = 2- 5/3 = 1/3 m = 1/ (x-1) ⇒ 1/3 = 1/(x-1) ⇒ x = 4 n = 1/(y-2) ⇒ 1/3 = 1/(y-2) ⇒ y = 5 Hence, x = 4 and y = 5