Answer :

We have


and


Lets simplify these equations. Assuming p = 1/(x + y) and q = 1/(x – y),



44p + 30q = 10 …(i)


Also,


55p + 40q = 13 …(ii)


To solve these equations, we need to make one of the variables (in both the equations) have same coefficient.


Lets multiply eq.(i) by 4 and eq.(ii) by 3, so that variable q in both the equations have same coefficient.


Recalling equations (i) & (ii),


44p + 30q = 10 [×4


55p + 40q = 13 [×3



11p = 1


p = 1/11


Substitute p = 1/11 in eq.(i)/eq.(ii), as per convenience of solving.


Thus, substituting in eq.(i), we get


44(1/11) + 30q = 10


4 + 30q = 10


30q = 10 – 4 = 6


q = 1/5


Thus, p = 1/11 and q = 1/5


As p = 1/(x + y),



x + y = 11 …(iii)


And q = 1/(x – y)



x – y = 5 …(iv)


Adding equations (iii) and (iv) to obtain x and y,


(x + y) + (x – y) = 11 + 5


2x = 16


x = 8


Putting the value of x in equation (iii), we get


8 + y = 11


y = 11 – 8


y = 3


Hence, we have x = 8 and y = 3


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