Question

22/(x+y)+15/(x-y)=5 ; 55/(x+y)+45/(x-y)=14​

Answer 1

Let 1/x+y=a and 1/x−y = b

Hence

22/x+y +15/x-y =5

→ 22a+15b=5 ...........(i)

and 55/x+y + 45/x-y = 14

→ 55a+45b=14.......(ii)

Multiply (i) by 3 and subtract from (ii) and get

11a=1 i.e a= 1/11

From (i)

b=(5−22a)/11

={5−22×(1/11)}/15= 1/5

Since 1/x+y=a

→ 1/x+y=1/11 i.e x+y =11

From (ii)

and 1/x−y = b

→ 1/x−y = 1/5 i.e x−y = 5 (iv)

Solving (iii) and (iv) gives x= 8 and y= 3