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Question
Solve the following simultaneous equations :
3(2u + v) = 7uv
3(u + 3v) = 11uv
Solution
3(2u + v) = 7uv
3(u + 3v) = 11uv
Dividing by uv, we get,
`(6)/v + (3)/u` = 7 ........(1)
3(u + 3v) = 11uv
3u + 9v = 11uv
Dividing by uv, we get
`(3)/v + (8)/u` = 11...........(2)
Multiplying (1) by 3, we get,
`(18)/v + (9)/u` = 21........(3)
Subtracting (2) from (3), we get,
`(15)/v` = 10
⇒ v = `(15)/(10) = (3)/(2)`
∴ `(3)/u`
= `7 - 6 xx (2)/(3)`
= 7 - 4
= 3
⇒ u = 1
Thus, the solution set is `(1,3/2)`.
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