Solve : 2 x + 3 y = 2 ; 4 x - 9 y = - 1 , x , y > 0

Given, 2 x + 3 y = 2 . . . . . i 4 x - 9 y = - 1 . . . . . i i Putting 1 x = u and 1 y = v , we get: 2 u + 3 v = 2 . . . . . i i i 4 u - 9 v = - 1 . . . . . i v On multiplying i i i by 2 , we get: 4 u + 6 v = 4 . . . . . v On adding ( i v ) and ( v ) , we get: 15 v = 5 ⇒ v = 1 3 1 y = 1 3 ⇒ y = 3 On substituting y = 3 in i , we get: 2 x + 3 3 = 2 2 x = 2 - 1 ⇒ 2 x = 1 x = 2 ⇒ x = 2 Hence, the required solution is x = 2 and y = 3