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Interchanged Coefficients Method

 

   Upasutra : Sankalana Vyavakalanaathyaam

   Meaning :  By addition and by subtraction

This sutra ( or upasutra ) is used when the x coefficients and the y coefficients are found interchanged. In this case the two equations are added and subtracted to obtain two simple simultaneous equations which on solving yield x and y.

Consider the following equations :

1)              43x - 21y = 129

                21x - 43y = 63

On adding,     64x -64y = 192

                 -->  x-y  = 192/64 = 3

On subtracting,      22x + 22y = 66

                -->  x + y = 66/22 = 3

                 -->  x + y = 3     and      x - y = 3

                 -->  x = 3  and   y = 0.


 2)            23x - 13y = 270

                 13x -  23y = 90

 On adding,     36x - 36y = 360

                   --> x - y = 10

 On subtracting,   10x + 10y = 180

                   --> x + y  = 18

   Hence on solving the following equations we get  x = 14 ,    y = 4.


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