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SAKALANA VYAVAKALANBHYAM

This Sutra means 'by addition and by subtraction'. It can be applied in solvinga special type of simultaneous equations where the x - coefficients and the y -

coefficients are found interchanged.

Example 1:

4x ! "#y $ %%# "#x ! 4y $ &%

In the conventional method we have to mae equal either the coefficient of xor coefficient of y in both the equations. (or that we have to multiply equation

) % * by 4 and equation ) " * by "# and subtract to get the value of x and thensubstitute the value of x in one of the equations to get the value of y or we have

to multiply equation ) % * by "# and equation ) " * by 4 and then subtract toget 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 thin of.

(rom Sanalana ! vyavaalanabhyam

add them,

i.e.+ ) 4x ! "#y * , ) "#x ! 4y * $ %%# , &% i.e.+ x ! y $ "/4 x ! y $ #

subtract one from other, i.e.+ ) 4x ! "#y * ! ) "#x ! 4y * $ %%# ! &% i.e.+ ""x , ""y $ "" x , y $ %

and repeat the same sutra+ we get x $ " and y $ - %

0ery simple addition and subtraction are enough+ however big thecoefficients may be.

Example 2: %&x ! 41y $ "4" 41x ! %&y $ -4&%#

2h 3 what a problem 3 nd still

5ust add+ "4#%) x ! y * $ - "4#% x ! y $ -%

subtract+ %41& ) x , y * $ 1#& x , y $

once again add+ "x $ 4 x $ "

subtract - "y $ - y $ #

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Solve the following problems using Sankalana Vavakalanabham!

1! "x # 2 $ 1% 2x # " $ 1&

2! 'x 21 $ 2(

21x ' $ 2(

"! (')x # )'( $ *1%( )'(x # (') $ "%%)