Vedic Mathematics | Sankalana-Vyavkalanabhyam
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 = 3
subtract one from other,
i.e., ( 45x – 23y ) – ( 23x – 45y ) = 113 – 91
i.e., 22x + 22y = 22
x + y = 1
and 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 = -1
subtract, 1479 ( x + y ) = 7395
x + y = 5
once again add, 2x = 4
x = 2
subtract - 2y = - 6
y = 3
Solve the following problems using
Sankalana – Vyavakalanabhyam.
1.
3x + 2y = 18
2x + 3y = 17
2.
5x – 21y = 26
21x – 5y = 26
3.
659x + 956y = 4186
956x + 659y = 3889