google.com, pub-6771220306917688, DIRECT, f08c47fec0942fa0
Latest Articles
Loading...

Info Post
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.

2 comments:

  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.

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

    ReplyDelete

Thank You for visiting Momscribe.com !
Your contribution is greatly appreciated.
Please feel free to subscribe to this blog either by Email or any methods listed on the right side of this content.

நன்றி ! மீண்டும் வருகை தாருங்கள் :)