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2015-05-16T15:59:32+05:30

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we eliminate the xy term.

8 y - 3 x = 5 x y          ---  equation  (1)

6 y - 5 x = - 2 x y            ---- equation (2)

multiply (1) by 2 and  multiply (2) with 5  and then add,

   16 y - 6 x  +  30 y  - 25 x =  10 x y  - 10 x y
   46 y - 31 x  = 0

   so  y = 31/46 * x        --- (3)

substitute this value of y in  (1).

         8 * 31/46 x  - 3 x  = 5 x * (31/46  x)

multiply by 46  and divide by  x  :

        248  -  138  =  155 x
           x  =  110 / 155 =  22/31
           y = 31/46 * 22/31  = 11/23
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another way:
    
    Divide equations (1) and (2)  by xy:

     8 / x  - 3 / y = 5         and      6 / x  - 5 / y = - 2

call 1/x = X  and  1/y  = Y

     8 X - 3 Y = 5        --- (3)
     6 X -  5 Y = -2        --- (4)

we eliminate X  by    (3)  * 3  -  (4) * 4

   24 X  - 9 Y -  24 X  + 20 Y  =  15  + 8
       11 Y = 23
   =>  Y = 23 /11          =>  y = 11/23
  substitute this in (3)
     
       8 X  -  3 * 23 /11 = 5
       8 X = 5 + 69/11  = 124/11
         X = 31/22

 => x = 22/31

2 5 2
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