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Question
Solve the following systems of equations:
`1/(7x) + 1/(6y) = 3`
`1/(2x) - 1/(3y) = 5`
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Solution
`1/(7x) + 1/(6y) = 3` ......(1)
`1/(2x) - 1/(3y) = 5` .......(2)
Multiplying (2) by 1/2 we get
`1/(4x) - 1/(6y) = 5/2` ....(3)
Solving (1) and (3), we get
`1/(7x) + 1/(6y) = 3`
`(1/(4x) - 1/(6y) = 5/2)/(1/(7x) + 1/(4x) = 3 + 5/2)` (Adding the equations)
`=> (4 + 7)/(28x) = (6 + 5)/2`
`=> 11/(28x) = 11/2`
`=> x= (11xx2)/(28xx11) = 1/14`
when x = 1/14 we get
`1/(7(1/14)) + 1/(6y) =3` using (1)
`=> 2 + 1/(6y) = 3`
`=> 1/(6y) = 3 - 2 =1`
`=> y = 1/6`
Thus, the solution of given equation is `x = 1/14 and y = 1/6`
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