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प्रश्न
Solve the following systems of equations:
`(7x - 2y)/(xy)` = 5
`(8x + 7y)/(xy)` = 15
बेरीज
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उत्तर
`(7x - 2y)/(xy)` = 5
⇒ `7/y - 2/x` = 5 ...(1)
`(8x + 7y)/(xy)` = 15
⇒ `8/y + 7/x` = 15 ...(2)
Let `1/x` = p and `1/y` = q
The given equations reduce to:
−2p + 7q = 5
⇒ −2p + 7q − 5 = 0 ...(3)
7p + 8q = 15
⇒ 7p + 8q − 15 = 0 ...(4)
Using the cross multiplication method, we obtain:
`p/(-105 - (-40)) = q/(-35 - 30) = 1/(-16 - 49)`
`p/(-65) = 1/(-65), q/(-65) = 1/(-65)`
p = 1, q= 1
`p = 1/x = 1, q = 1/y = 1`
x = 1, y = 1
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