The given equations are:
x + y = 5xy …..(i)
3x + 2y = 13xy ……(ii)
From equation (i), we have:
x + y/ xy = 5
⇒ 1/y + 1/x = 5 ……(iii)
For equation (ii), we have:
3x + 2y/xy = 13
⇒ 3/y + 2/x = 13 ……(iv)
On substituting 1/y = v and 1/x = u, we get:
v + u = 5 ……(v)
3v + 2u = 13 …….(vi)
On multiplying (v) by 2, we get:
2v + 2u = 10 ….(vii)
On subtracting (vii) from (vi), we get:
v = 3
⇒ 1/y = 3
⇒ y = 1/3
On substituting y = 1/3 in (iii), we get:
1/ 1/ 3 + 1/x = 5
⇒ 3 + 1/x = 5
⇒ 1/x = 2
⇒ x = 1/2
Hence, the required solution is x = 1/2 and y = 1/3 or x= 0 and y = 0.
