We have

and

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

10p + 2q = 4 …(i)

Also,

⇒ 15p – 9q = - 2 …(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 9 and eq.(ii) by 2, so that variable q in both the equations have same coefficient.

Recalling equations (i) & (ii),

10p + 2q = 4 [×9]

15p – 9q = - 2 [×2]

⇒ 120p = 32

⇒ p = 4/15

Substitute p = 4/15 in eq.(i)/eq.(ii), as per convenience of solving.

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

15(4/15) – 9q = - 2

⇒ 4 – 9q = - 2

⇒ 9q = 4 + 2 = 6

⇒ q = 2/3

Thus, p = 4/15 and q = 2/3

As p = 1/(x + y),

⇒

⇒ 4x + 4y = 15 …(iii)

And q = 1/(x – y)

⇒

⇒ 2x – 2y = 3 …(iv)

Multiplying eq.(iv) by 2, we get

4x – 4y = 6 …(v)

and then adding equations (iii) and (v) to obtain x and y,

(4x + 4y) + (4x – 4y) = 6 + 15

⇒ 8x = 21

⇒ x = 21/8

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

2(21/8) – 2y = 3

⇒ 21/4 – 2y = 3

⇒ 2y = 21/4 – 3 = 9/4

⇒ y = 9/8

Hence, we have x = 21/8 and y = 9/8