Anurupye - Sunyamanyat

The Sutra Anurupye Sunyamanyat says : "If one is in ratio, the other one is zero".

We use this Sutra in solving a special type of simultaneous simple equations
in which the coefficients of 'one' variable are in the same ratio to each other
as the independent terms are to each other. In such a context the Sutra says
the 'other' variable is zero from which we get two simple equations in the first
variable (already considered) and of course give the same value for the variable.

Example 1: 

 3x + 7y = 2

 4x + 21y = 6

Observe that the y-coefficients are in the ratio 7 : 21 i.e., 1 : 3, which is

 same as the ratio of independent terms i.e., 2 : 6 i.e., 1 : 3. Hence the other

 variable x = 0 and 7y = 2 or 21y = 6 gives y = 2 / 7


Example 2:

323x + 147y = 1615

969x + 321y = 4845

The very appearance of the problem is frightening. But just an observation

and anurupye sunyamanyat give the solution x = 5, because coefficient of x

ratio is

323 : 969 = 1 : 3 and constant terms ratio is 1615 : 4845 = 1 : 3.

y = 0 and 323 x = 1615 or 969 x = 4845 gives x = 5.