Solve for x and y:
We have
and
Lets simplify these equations. Assuming p = 1/(x + y) and q = 1/(x – y),
5p – 2q = - 1 …(i)
Also,
⇒ 15p + 7q = 10 …(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 3, so that variable p in both the equations have same coefficient.
Recalling equations (i) & (ii),
5p – 2q = - 1 [×3
15p + 7q = 10
⇒ - 13q = - 13
⇒ q = 1
Substitute q = 1 in eq.(i)/eq.(ii), as per convenience of solving.
Thus, substituting in eq.(i), we get
5p – 2(1) = - 1
⇒ 5p – 2 = - 1
⇒ 5p = 2 – 1 = 1
⇒ p = 1/5
Thus, p = 1/5 and q = 1
As p = 1/(x + y),
⇒
⇒ x + y = 5 …(iii)
And q = 1/(x – y)
⇒
⇒ x – y = 1 …(iv)
Adding equations (iii) and (iv) to obtain x and y,
(x + y) + (x – y) = 5 + 1
⇒ 2x = 6
⇒ x = 3
Putting the value of x in equation (iii), we get
3 + y = 5
⇒ y = 2
Hence, we have x = 3 and y = 2