how to solve linear equations,what is linear equations, How to solve linear equations,Graphical Method and Algebraic Methods

What is linear equations ?

Linear equations :- Two linear equations in the same two variables are called a pair of linear equations in two variables. The most general form of a pair of linear equations is

 

Where a1, a2, b1, b2, c1, c2  are real numbers, such that     

How to solve linear equations ?

Method of solving linear equation of two variables

A pair of linear equations in two variables can be represented, and solved, by the:

(i)graphical method             (ii) algebraic method

All in one table for this chapter

If a pair of linear equations are

Then

S.N.	Compare the Ratio	Graphic representation	Algebraic interpretation	Linear equations
1		Intersection lines at one point	Exactly one solution or unique solution	Consistent
2		Coincident line	Infinity solution or many solutions	Dependent and consistent
3		Parallel lines	No solution	Inconsistent

Conclusion from the  table

Graphical Method :

The graph of a pair of linear equations in two variables is represented by two lines.

(i) If the lines intersect at a point, then that point gives the unique solution of the two equations. In this case, the pair of equations is consistent.

(ii) If the lines coincide, then there are infinitely many solutions — each point on the line being a solution. In this case, the pair of equations is dependent (consistent).

(iii) If the lines are parallel, then the pair of equations has no solution. In this case, the pair of equations is inconsistent.

Algebraic Methods : 

 We have discussed the following methods for finding the solution(s) of a pair of linear equations :

(i) Substitution Method

(ii) Elimination Method

(iii) Cross-multiplication Method

Formula of cross multiplication is