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2014-05-23T12:38:37+05:30

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Given 
99x+101y = 499------------> 1
101x+99y = 501-----------------> 2 
multiply equation 1 with 101 
then we get  (99x+101y = 499)101
⇒9999x+10201y=50399----------------> 3
Now let us consider 2nd equation 
multiply 2nd equation by 99 
then we get (
101x+99y = 501)99
⇒9999x+9801y=49599---------------> 4
solving 3 & 4 we get 

400y = 800
⇒y = 2 
Now substitute y = 2 in equation 1 
then we get the value of x 
99x+101*2=499
99x+202=499
99x=297
x=3
4 4 4