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प्रश्न
Solve the following simultaneous equation :
8v - 3u = 5uv
6v - 5u = -2uv
उत्तर
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)`.
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