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,

⇒ 3p + 2q = 12 …(i)

⇒ 2p + 3q = 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 2 and eq.(ii) by 3, so that variable p in both the equations have same coefficient.

Recalling equations (i) & (ii),

3p + 2q = 12 [×2

2p + 3q = 13 [×3

⇒ - 5q = - 15

⇒ q = 3

Substitute q = 3 in eq.(i)/eq.(ii), as per convenience of solving.

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

3p + 2(3) = 12

⇒ 3p + 6 = 12

⇒ 3p = 12 – 6 = 6

⇒ p = 2

Thus, p = 2 and q = 3

As p = 1/x,

⇒ 2 = 1/x

⇒ x = 1/2

And q = 1/y

⇒ 3 = 1/y

⇒ y = 1/3

Hence, we have x = 1/2 and y = 1/3