# Solve for x and y

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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