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SAŃKALANA – VYAVAKALANĀBHYAM
This Sutra means 'by addition and by subtraction'. It can be applied in
solving a special type of simultaneous equations where the x - coefficients and
the y - coefficients are found interchanged. Example 1: 45x – 23y = 113 23x – 45y = 91 In the conventional method we have to make equal either the coefficient of x or coefficient of y in both the equations. For that we have to multiply equation ( 1 ) by 45 and equation ( 2 ) by 23 and subtract to get the value of x and then substitute the value of x in one of the equations to get the value of y or we have to multiply equation ( 1 ) by 23 and equation ( 2 ) by 45 and then subtract to get value of y and then substitute the value of y in one of the equations, to get the value of x. It is difficult process to think of. From Sankalana – vyavakalanabhyam add them, i.e., ( 45x – 23y ) + ( 23x – 45y ) = 113 + 91 i.e., 68x – 68y = 204  x – y = 3subtract one from other, i.e., ( 45x – 23y ) – ( 23x – 45y ) = 113 – 91 i.e., 22x + 22y = 22 x + y = 1and repeat the same sutra, we get x = 2 and y = - 1 Very simple addition and subtraction are enough, however big the coefficients may be. Example 2: 1955x – 476y = 2482 476x – 1955y = -4913 Oh ! what a problem ! And still just add, 2431( x – y ) = - 2431 x – y = -1subtract, 1479 ( x + y ) = 7395 x + y = 5once again add, 2x = 4 x = 2subtract - 2y = - 6 y = 3 1. 3x + 2y = 18 2x + 3y = 17 2. 5x – 21y = 26 21x – 5y = 26 3. 659x + 956y = 4186 956x + 659y = 3889 |
