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Question
Solve the following systems of equations:
`"xy"/(x + y) = 6/5`
`"xy"/(y- x) = 6`
Solution
The given system of equation is
`"xy"/(x + y) = 6/5`
=> 5xy = 6(x + y)
=> 5xy = 6x + 6y ....(i)
And `(xy)/(y - x) = 6`
=> xy = 6(y -x)
=> xy= 6y - 6x ....(ii)
Adding equation (i) and equation (ii), we get
6xy = 6y + 6y
=> 6xy = 12y
`=> x = (12y)/(6y) = 2`
Putting x = 2 in equation (i), we get
`5 xx 1 xx y = 6 xx 2 + 6y`
=> 10y = 12 + 6y
=> 10y - 6y = 12
=> 4y = 12
`=> y = 12/4 = 3`
Hence, solution of the given system of equation is x = 2, y =3
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