Friday, 27 April 2012

Solve simultaneous linear equations easily

The vedic maths sutra to be used: "If one is in ratio, the other one is zero"

While trying to solve simultaneous equations, especially with bigger numbers, you can use this vedic math sutra to simplify the process.

There is a precondition for using this formula though, and it is that there has to be a linear relationship with ratio of coefficient of one of the unknown in the equation with the constant term. For all the linear equations satisfying this condition, can be solved by simply putting the other unknown (other than the one with ratio of coefficients in proportion of the constant) as zero.


5x + 8y = 24
23x + 16y = 48

In these equations, we have two unknown (x & y), so let us test if any of them satisfy the required condition:

Testing for x
Ratio of coefficients of x = 23 / 5 = 4.6
Ratio of constant number = 48 / 24 = 2
Not satisfied for x.

Testing for y
Ratio of coefficients of y = 16 / 8 = 2
Ratio of constant number = 48 / 24 = 2
Satisfied for y.

Therefore, the solutions to this equation is x = 0 and therefore y = 3.

however, if both the unknown satisfy the condition, then the equations can not be solved.

The Logic:
The equations consist of two sides LHS and RHS.
Now, RHS is a constant number the ratio of increase is RHS is obvious and can be understood just by observation, which in this case is 2.

This reflects that the LHS of second equation has to deliver a value exactly double as compared to what LHS to first equation delivered.

Now, LHS comprises of two terms with unknown x & y and having different coefficients. For LHS to second equation to become exactly double as compared to the first, both the coefficients should double. But in this case, y is exactly doubling and x is increasing randomly, which clearly means that whatever be the coefficient of x, it has to be zero so as not to disturb the proportion.

Now enjoy solving simultaneous liner equations just by looking at them with the use of this vedic math sutra.


  1. Thank you for dropping. I appreciate it.

    Bouncing on Words

  2. Vedic maths is very popular now days.The education boards have included this subject in the course of students.It enhances the memory power.CBSE has posted different sample papers for board exam aspirants like cbse board sample papers for history.If anybody wants paper of any subject,they can download it .

  3. Sir, how to solve Linear Equations with three variables?
    Can you please explain the problem I was mentioning below:

    7x+6y+4z = 122,
    4x+5y+3z = 88,
    9x+2y+z = 78.


    1. The answers are x=6, y=8, and z=8 .
      First Eliminate Z first of all .
      Solve x and y .
      Put value of x and y and get the value of z.