Solve for x and y:

We have

and

where x≠0 and y≠0

Lets simplify these equations. Assuming 1/x = p and 1/y = q, we can rewrite them,

⇒ 9p – 4q = 8 …(i)

⇒ 13p + 7q = 101 …(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 7 and eq.(ii) by 4, so that variable q in both the equations have same coefficient.

Recalling equations (i) & (ii),

9p – 4q = 8 [×7

13p + 7q = 101 [×4

⇒ 115p = 460

⇒ p = 4

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

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

9(4) – 4q = 8

⇒ 36 – 4q = 8

⇒ 4q = 36 – 8 = 28

⇒ q = 7

Thus, p = 4 and q = 7

As p = 1/x,

⇒ 4 = 1/x

⇒ x = 1/4

And q = 1/y

⇒ 7 = 1/y

⇒ y = 1/7

Hence, we have x = 1/4 and y = 1/7