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# If one is in ratio, the other one is zero

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Using this formula we can solve simultaneous linear equations which may involve big numbers.In special cases,we can solve these equations by just looking at it.

Example 1:

5x + 4y =6
27x + 20 y =30

Observe the above equation carefully.You can notice that the ratio of coefficients of y is same as that of the constant terms .i.e;coefficients of y is 4 :20  i.e; 1:5 which is same as the constant terms 6:30 i.e; 1:5 .Hence we put x = 0.
Put x =0 in any equation above and calculate mentally the value of  y. Doing the same in the first equation we get y= 6/4.

Example 2:

2 x + 4 y =3
16x+5y=24

Here, coefficients of x is 2:16 i.e; 1:8 which is same as the constant term 3:24 .i.e; 1:8 meaning that the ratio of coefficients of x is same as that of the constant terms .So we put  y = 0 in any equation above.
Soving the above equations we get the value of x = 3/2

Example 3:

In solving simultaneous quadratic equations too, we can make use of this sutra
Solve x + 4y = 10 and  x2 + 5xy + 4y2 + 4x - 2y = 20 ?
First lets simplify this  x2 + 5xy + 4y2 + 4x - 2y = 20
= ( x + y ) ( x + 4y ) + 4x – 2y = 20

= 10 ( x + y ) + 4x – 2y = 20 ( Since x + 4y = 10 )

= 10x + 10y + 4x – 2y = 20
= 14x + 8y = 20

Now comparing these two equations x + 4y = 10  and 14x + 8y=20 ,we see that coefficients of y is same that of the constant term(
4 : 8 :: 10 : 20) so we put x=0 to get the value of y.Therefore,value of y = 5/2

Note:
This technique works  ONLY when either the co-efficients of x or y equals to that of the constant terms.This can be extended to more general cases with any number of variables

Example :
ax + by + cz = a
bx + cy + az = b
cx + ay + bz = c
which yields x = 1, y = 0, z = 0 since the coefficients of x is same that of the constant terms.

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1. Uma,
Wow, I am very happy that you visited my blog and thanks for the lovely comments.
One more reason to be happy is we both have a common interest i.e. Vedic Maths. I have done the course and I love it. I always use it and its my favorite.
Keep Visiting and for me, I am a follower from now.
I always thought of posting about Vedic Maths in my blog, but I am not able to manage the time.

2. @nivedita -thanks for your lovely comment.Lets c what we can do :D

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