Answer 1

`2/x + 3/y = 13` ; `5/x - 4/y = -2`
Let `1/x = u and 1/y = v`
So, the equations obtained are
2u + 3v = 13                        ........(I)       ( x 5)
5u - 4v = -2                         .........(II)      ( x 2)
10u + 15v = 65                   ..........(III)
10u - 8v = - 4                     ...........(IV)
Subtracting (IV) from (III)
23v = 69
⇒ v = 3
Putting the value of v in (I)
2u + 3 x 3 = 13
⇒ 2u = 4
⇒ u =2
`1/x = u ⇒ x = 1/u = 1/2`
`1/y = v  ⇒ y = 1/v = 1/3`