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 x

^{2}+ 5xy + 4y

^{2}+ 4x - 2y = 20 ?

First lets simplify this x

^{2}+ 5xy + 4y

^{2}+ 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.
Uma,

ReplyDeleteWow, 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.

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

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