Vedic Mathematics/Sutras/(Anurupye) Shunyamanyat

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.

The very appearance of the problem is frightening. But just an observation and Anurupye Sunyamanyat gives us the solution