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Solve the following system of equatio...

Solve the following system of equations: `(7x-2y)/(x y)=5,\ \ \ (8x+7y)/(x y)=15`

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We have
` ( 7x - 2y)/( xy ) = 5 rArr ( 7)/(y) - (2)/(x) = 5 " " `… (i)
` ( 8 x+ 7y )/(xy) = 15 rArr ( 8)/(y) + ( 7)/(x) = 15 " " ` … (ii)
Multiplying (i) by 7 and (ii) by 2 and adding the results, we get
` ((49)/(y) + (16)/(y)) = ( 35 + 30)`
` rArr ( 65)/( y ) = 65 rArr 65 y = 65 rArr y = 1 `
Putting `y = 1 ` in ( ii), we get
` ( 8)/(1) + ( 7)/(x) = 15 rArr ( 7)/(x) = ( 15 - 8) = 7 rArr 7x = 7 rArr x = 1 `
Hence, ` x = 1 and y = 1 `.
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