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Pair of linear Equations in two Variables

Firstly we must be awear about the Pair of linear equations in two variables

VARIABLE is the mathematical quantity taking any value depends upon the condition. And are represented by The alphabets..

Here the question arises Is x variable or the Alphabet?

X is an alphabet but is used for the representation of the varibales.

We have two ways to solve pair of linear equations in two variables

1. Graphical or geometrical method.

2. Algebraical Method. In geometrical or graphical method firstly we must need to find the ratio of the coefficients of the varibales in both the equations.Here arises three cases about the solution of the pair of linear equations a1x + b1y + c1=0    (1) a2x + b2y + c2= 0   (2)

I) Unique Solution a1/a2 != b1/b2 When the equations have unique solution then the graph of given equations will be intersecting lines and are said to be Consistant equations.

II) infinitely many Solutions a1/a2 = b1/b2 =c1/c2 When the equations have infinitely many solutions then the graph of given equations will be Coincident lines and are said to be Dependent equations. So No Need to find the Solution By Algebraic method.

III) No Solution a1/a2 = b1/b2 !=c1/c2 When the equations have no solutions then the graph of given equations will be Parallel lines and are said to be Inconsistent equations. So No Need to find the Solution By Algebraic method.

Algebraical Method for solving Pair of linear equations in two variables: There are three algebraical methods for solving Pair of linear equations in two variables:

1. SUBSTITUTION METHOD

2. ELIMINATION METHOD

3. CROSS MULTIPLICATION METHOD