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

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