Sankalana – Vyavakalanabhyam

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.