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Question
Solve the following systems of equations:
`(7x - 2y)/"xy" = 5`
`(8x + 7y)/"xy" = 15`
Solution
`(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 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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