1.

Solve for x and y : ` (xy )/(x + y ) = ( 6)/(5), (xy)/( y - x) = 6 (x ne 0, y ne 0 and x ne y )`.

Answer» The given equations may be written as
` (x + y )/( xy) = ( 5)/(6) rArr (1)/(y) + ( 1)/(x) = ( 5)/(6)" " `… (i)
` ( y - x )/( xy ) = (1)/(6) rArr (1)/(x) - (1)/(y) = (1)/(6) " " `… (ii)
Adding (i) and (ii), we get
` (2)/(x) = (( 5)/(6) + (1)/(6)) = (6)/(6) = 1 rArr x = 2 `
Subtracting (ii) from (i), we get
`(2)/(y)= ((5)/(6) - (1)/(6)) = ( 4)/(6) = (2)/(3) rArr y = 3 `
Hence, ` x = 2 and y = 3 `.


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