13Jan07-5 second solving for x & y equations!

Today I learnt a very simple method of solving an equation with 2 variables but with a specific property.

Consider the eqns below:

5x+13y = 25
15x+7y = 75

Traditional way:
x=(25-13y)/5
3(25-13y) + 7y = 75
75-39y+7y = 75
-32y = 0
hence y = 0
and x = 5

The Vedic Way:
5x+13y = 25
15x+7y = 75

if the eqns appear in such a format that the ratio of the constants of x or that of y are in the same ratio as that of the RHS constantsthat is 5/15 or 13/7 = 25/75..........in this case 5/15 = 25/75
therefore we can directly say that the other variable ie y = o and x will be 5

Another eg:
6x=7y = 8
19x 14y = 16
looking at this eqns we can say that 7/14 is the same ratio as 8/16therfore x = 0 and y = 8/7