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2014-12-01T04:22:16+05:30

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Call  u = 1/x    and  v = 1/y

 41 u - 4 7 v =  35   -- equation 1

 47 u - 41 v = 53  -- equation 2

   Multiply the first equation by 47 and second by 41 and then subtract equation 2 from equation 1,  we get

     41 * 47 u - 47 * 41 u - 47² v + 41² v = 47* 35 - 53 * 41
       - 528 v = -528
             v = 1
   substituting in equation 1, we get ,
      
         41 u - 47 = 35    =>    u = 82/41 = 2

 1/x = u = 2  =>  x = 1/2 
    1/y = v = 1    =>  y =  1

1 5 1
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