Anurupye - Shunyamanyat

If one is in ratio, the other is zero

Anurupye - Shunyamanyat is the sixth sutra of Vedic mathematics. Its corollary is Yavadunam Tavadunam.

This sutra is used in solving simultaneous simple equations in which one of the unknown terms are in the same ratio to each other as the independent terms are in ratio to each other. This is very rarely useful but saves much time when it can be used. I'll give an example:
Solve for y and z in the following two equations in which y and z have the same value in both equations:
28,000,000z + 30,000y = 5,000,000
39,000,000z + 90,000y = 15,000,000
Observe that the y-coefficients are in the ratio 1:3, and that the independent terms (3 million and 15 million) are also in that same ratio.
This sutra, "If one is in ratio, the other is zero", would lead us to assume z = 0 and we would then simplify the problems and solve for y
30,000y = 5,000,000 and 90,000y = 15,000,000
y = 5,000,000/30,000 and y = 15,000,000/90,000
In both cases, y = 166.6666repeating

Anurupye - Shunyamanyat can also be applied to a limited number of simultaneous quadratic equations. To learn more about this sutra, check out the resources below:

Vedic Mathematics by Sri Bharati Krisna Tirthaji
Mathemagics by Arthur Benjamin and Michael B. Shermer