We have

x + y = 5xy

and 3x + 2y = 13xy

where x≠0 and y≠0

Lets simplify these equations.

x + y = 5xy

Dividing the equation by xy throughout,

⇒

Assuming p = 1/y and q = 1/x, we get

p + q = 5 …(i)

Also, 3x + 2y = 13xy

Dividing the equation by xy throughout,

⇒

Assuming p = 1/y and q = 1/x, we get

⇒ 3p + 2q = 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, so that variable q in both the equations have same coefficient.

Recalling equations (i) & (ii),

p + q = 5 [×2]

3p + 2q = 13

⇒ - p = - 3

⇒ p = 3

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

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

3 + q = 5

⇒ q = 5 – 3

⇒ q = 2

Thus, p = 3 and q = 2

As q = 1/x,

⇒ 2 = 1/x

⇒ x = 1/2

And p = 1/y

⇒ 3 = 1/y

⇒ y = 1/3

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