Page 20 - VEDIC MATHEMATICS

16x + 96y =16 12x + 5y = 96 7x – 9y = 36

Sutra 7 - 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

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

CLASS VIII – Exercise – 10
Solve the following problems usingSankalana – Vyavakalanabhyam.

1. 3x + 2y = 18 2x + 3y = 17
2. 5x – 21y = 26 21x – 5y = 26

3. 659x + 956y = 4186 956x + 659y = 3889

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