Solve equations easily and fast

The vedic maths sutra to be used: "Adjust After Transposing (Paravartya Yojayet)"

When students are introduced to the concept of solving equations, the first method taught for solving basic equations is as follows:

Let us say we want to solve the equation 3x - 9 = 0

3x - 9 = 0

3x = 9 (transposing 9 to the other side of equation)

x = 9 / 3 (adjusting 3 with 9 on the right hand side of the equation)

x = 6 (Solution of equation)

This method is little lengthy and can not be used quickly for solving complex equations. Vedic mathematics has a sutra for solving equations and is based on the same concept of transposing and then applying. (Paravartya = Transpose; Yojayet = Adjust)

So let us understand this vedic math trick to solve equations fast and easily.

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.

Let us just analyse our normal method of solving equations and see how it actually gives us an answer.

Let us say, we want to solve an equation

ax + b = px + q

ax - px = q - b (transposing both the sides)

x (a - p) = q - b

x = (q - b) / (a - p) (adjusted both the sides)

Thus, every equation that we want to solve using this lengthy method, can be solved easily just by using the final solution that x = (q - b) / (a - p)

Example 1:

5x + 8 = 3x + 16

Without getting into any lengthy calculation, let us solve this equation by using the vedic math trick, the answer would be:

x = (16 - 8) / (5 - 3)

x = 4

Example 2:

4x - 6 = 3x + 16

x = (16 + 6) / (4 - 3)

x = 22

Isn't it simple solving equations using this method instead of getting into length calculations.

Now let us consider solving tricky equations with the same method.

1. Solving equations with undefined solutions

Example 3:

4x + 6 = 4x + 16

x = (16 - 6) / (4 - 4)

x = Undefined (This equation involved division by 0, hence the solution to this equation is undefined as it should be)

2. Solving equations expressed as ratio to one another

While solving equation expressed as ratio to one another, the solution as per vedic math trick would change a little bit as follows:

(ax + b) / (px + q) = y / z

x = (yq - zb) / (za - yp)

Example 4:

(3x + 5) / (6x + 4) = 7 / 8

x = (7*4 - 8*5) / (8*3 - 7*6)

x = (28 - 40) / (24 - 42)

x = (-12) / (-18)

x = 2 /3 (This solution can be checked by trying the traditional method)

Similarly, if (6x + 4) / (3x + 2) = 2, then the same vedic math trick can be used to solve this formula just by replacing 2 with (2/1) on the right hand side of the equation.

When faced with equations such as (2x + 3) / x = 13 / 5, the same vedic math trick can be used and we just need to rewrite the given equation in the format we have the solution, refer the below example.

Example 5:

(2x + 3) / x = 13 / 5

(2x + 3) / (1x + 0) = 13 / 5 (Rewritten the equation to match with the vedic math trick)

x = (13*0 - 5*3) / (5*2 - 13*1)

x = (0 - 15) / (10 - 13)

x = (-15) / (-3)

x = 5 (This solution can be checked by trying the traditional method)

Thus, any equation with single power of the unknown can be easily solved using this vedic math tricks. We just have to make sure to rewrite the equation in the structure provided by the vedic math trick adjust after transposing.

Solving equations is so easy ans fast with the help of vedic math tricks!

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.

Example:

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.

Solve quadratic equations easily with vedic maths

The vedic math sutra used for simplifying equations is : "It is zero if the Samuccaya is Same"

This formula aims to simplify the solution of quadratic equations by setting some simple ground rules. But, before we understand the application of this vedic math sutra with quadratic equation, let us start with basic equations and understand the applicability of this vedic mathss sutra.

This vedic math sutra (It is zero if the Samuccaya is same) has applicability in four different situations:

1. When a common term is there on all the terms of left hand side as well as right hand side of an equation, then that equation can be solved by assuming that common term to be zero.

Example:

11x + 5x = 6x + 7x

Since "x" occurs as a common factor in all the terms (of both LHS & RHS), therefore, x = 0 is a solution.

2. When multiplication of all the numbers appearing on each side of the equation is equal, the solution to that equation can be derived by assuming the unknown to be zero. 

Example:

(x + 6) (x + 5) = (x + 3) (x + 10)

6 * 5 = 3 * 10 (multiplication of each side's numbers is equal = 30)

Solution is x = 0

3. The sum of the fractions with same numerical numerator can be derived by adding the denominators and equating it to zero.

Example:

3/ (4x − 1) + 3/ (6x − 1) = 0

In this case the numerator of both the fractions is the same number 3, therefore the addition can be re-written as:

10x-2 = 0 (LHS simplified by adding the denominators)

x = 1/5

4.  For a quadratic equation expressed as N1/D1 = N2/D2 and if N1 + N2 = D1 + D2, then this sum (i.e. either N1+N2 or D1+D2) is zero. This would help solve the quadratic equation easily.

Example:

(3x + 8) / (3x + 4) = (3x + 4) / (3x + 8)

In this case, the condition can be assessed as:

N1 + N2 = 3x + 8 + 3x + 4 = 6x + 12

D1 + D2 = 3x + 4 + 3x + 8 = 6x + 12

N1 + N2 = D1 + D2

Therefore,

N1 + N2 = D1 + D2 = 0

6x + 12 = 0

x = -2 (Solution to quadratic equation)

Now with the knowledge of this vedic math sutra solving quadratic equation faster is very easy.