Question

Solve the following simultaneous equations :
2(3u - v) = 5uv
2(u + 3v) = 5uv

Answer 1

2(3u - v) = 5uv
2(u + 3v) = 5uv
2(3u - v) = 5uv
⇒ 6u - 2v = 5uv
⇒ `(6)/v - (2)/u` = 5..........(1)
2(u + 3v) = 5uv
⇒ 2u + 6v = 5uv
⇒ `(2)/u + (6)/v` = 5........(2)
Multiplying equation (1) by 3, we get,
`(18)/v - (6)/u` = 15..........(3)
Adding (2) and (3),
`(20)/v` = 20
⇒ v = 1
∴ `(6)/u`
= `5 - (2)/(1)`
= 3
⇒ u = `(6)/(3)`
= 2
Thus, the solution set is (2, 1).