Question

Solve for x and y:
x + y = 5xy, 3x + 2y = 13xy

Answer 1

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.`