## Vedic Math Simultaneous Equation

In this topic we will study how to solve Simultaneous Linear Equations. The need to solve these equations arise while cracking word-problems frequently asked in all types of competitive exams

## What are simultaneous linear equation?

Simultaneous Linear Equations have two variables in them. Let say 'x' & 'y'. Since there are two variables in the equation we cannot solve it by itself. We need another equation with the same variable values to find the answer. When these two equations are solved together we get the values of variables 'x' & 'y'.

##### Simultaneous Equations - General Type

The Vedic Method we uses sutra "Paravartya" which is applicable to all cases and the special Sutras are applicable only to special types of cases. The Vedic method enables us to give the answers immediately.

In this method we will not be forming new equation but instead we will calculate the values of 'x' & 'y' with the given equations only. The value of the variable 'x' & 'y' will be expressed in the form of numerator upon denominator

X** = Numerator/Denominator & y = Numerator/Denominator**

For the value of 'x', we start with the y-coefficient and the constant term and cross multiply forward i.e. rightward (i.e. we start from the upper row and multiply across by the lower one ; and conversely ; and the connecting link between the two cross products is always minus). And that gives us our Numerator

##### Simultaneous Equations - Type 01

There is a special type of Simultaneous Linear Equations which may involve big numbers and may therefore seem hard but owing to a certain ratio between the coefficients, can be readily i.e. mentally solved with the aid of Sutra "Sunyam Anyat" (which cryptically says : If one is in ratio, the other one is zero)

##### Simultaneous Equations - Type 02

There is another specials type of Simultaneous Linear Equations where the x-coefficient and the y-coefficient are found interchanged. No elaborate multiplication etc, are needed here. The (axiomatic) Upasutra "Sankalana Vyavakalanabhyam" (which means "By addition and by subtraction" gives us immediately two equations giving the values of (x + y) and (x - y). And the repetition of the same process gives us the values of 'x' & 'y'. And the whole work can be done mentally.