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
From Sankalana – vyavakalanabhyam
add them,
i.e., ( 45x – 23y ) + ( 23x – 45y ) = 113 + 91
i.e., 68x – 68y = 204 i.e., x – y = 3
subtract one from other,
i.e., ( 45x – 23y ) – ( 23x – 45y ) = 113 – 91
i.e., 22x + 22y = 22 i.e., x + y = 1
and repeat the same sutra, we get x = 2 and y = - 1
Example 2:
1955x – 476y = 2482
476x – 1955y = -4913
Oh ! what a problem ! And still
just add, 2431( x – y ) = - 2431 i.e., x – y = -1
subtract, 1479 ( x + y ) = 7395 i.e., 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
