Question

Solve the following simultaneous equation :
8v - 3u = 5uv
6v - 5u = -2uv

Answer 1

8v - 3u = 5uv
6v - 5u = -2uv
Dividing both sides of each equation by uv, we get,
`(8)/u - (3)/v` = 5..........(1)

`(6)/u - (5)/v` = -2.........(2)
Multiplying (1) by 3 and (2) by 4, we get,
`(24)/u - (9)/v` = 15.......(3)

`(24)/u - (20)/v` = -8........(4)
Subtracting (4) from (3), we get,
`(11)/v` = 23

⇒ v = `(11)/(23)`

∴ `(6)/u - (5)/(11) xx 23` = -2

⇒ `(6)/u - (115)/(11)` = -2

⇒ `(6)/u`

= `-2 + (115)/(11)`

= `(-22 + 115)/(11)`

= `(93)/(11)`

⇒ u = `(6 xx 11)/(93)`

= `(22)/(31)`

Thus, the solution set is `(22/11 , 11/23)`.