## Cyclic (General) Formula

This is a GENERAL formula of Vedic Mathematics which can be applied to any 2 equations for obtaining 2 unknown values.

Consider following 2 general equations

ax + by = p

cx + dy = q

Solving,

x = (bq – pd) / (bc – ad)

y = (cp – aq) / (bc – ad)

Notice that for calculation of numerators (x any y) cyclic method is used and Denominators remains same for both x and y.

Examples:

2x + 3y =6

3x + 4y = 3

Applying above formula:

x = (9 – 24)/ (9 – 8) = -15

y = (18 – 6) (9 – 8) = 12

-3x + 5y = 2

4x + 3y = -5

Applying above formula:

x = (-25 -6) / (20+9) = -31/29

y = (8-15) / (20+9) = -7/29

## Sunyam Anyat

### Sanskrit Name:

शून्यमन्यत्

### English Translation:

If one is in ratio then other is 0.

### Prerequisites:

Ratio of 1 of the variables should be = ratios of RHS.

### Meaning:

If above condition is satisfied then other variable = 0.

The variable which was in ratio = Ratio of RHS and its corresponding coefficient.

### Examples:

3x + 2y = 4

6x + 3y = 8

Here coefficients of (x) are in ratio 1:2 which is same as that of RHS.

So according the Sunyam Anyat, y= 0.

And x is calculated by taking the ratio of RHS and coeff i.e. 4/3 or 8/6. Hence x = 4/3.

12x + 8y = 7

16x + 16y = 14 Here coeff of y and RHS are in same ratio. So x = 0 and y = 7/8.

## Sankalana Vyavakalanabhyam

### Sanskrit Name:

संकलनव्यवकलनाभ्याम्

### English Translation:

Addition and Subtraction.(Addition and Subtraction gives x+y and x-y expressions).

### Prerequisites:

Coefficient of 1 variable in 1st equation should be same to other in 2nd equation (+/- matterless.)

### Meaning:

If coefficient of 1 variable 1st equation is same as that of other in 2nd equation then Adding and Subtracting both the equations brings equations in the form of ‘x+y’ and ’x-y’ which can be EASILY solved simultaneously.

### Examples:

2x + 3y = 5

3x + 2y = 6

Adding both Equations gives, 5x + 5y = 11. Hence x + y = 11/5.

Subtracting both equation gives, -x + y = -1

Now these 2 new equations can be EASILY solved simultaneously giving x = 8/5 and y = 3/5.

Similarly solve for 23x – 14y = 34 & 14x – 23y = 12.

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