- Home
- CBSE 8TH
- CBSE 9TH
- CBSE 10TH
- CBSE NCERT Books
- CBSE 11TH
- CBSE 12TH
- Forum
- IndiaCBSE Blog
- CBSE Exam Results
- CBSE Helpline

# CBSE 10th Maths Chap 3 - PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

**Chapter Summary
**

**
**1. 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

a

_{1}x + b

_{1}y + c

_{1}= 0

a

_{2}x + b

_{2}y + c

_{2}= 0

where a

_{1}, a

_{2}, b

_{1}, b

_{2}, c

_{1}, c

_{2}are real numbers, such that a

_{1}

^{2}+b

_{1}

^{2}≠ 0, a

_{2}

^{2}+b

_{2}

^{2}≠ 0.

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

(i) graphical method

(ii) algebraic method

3. 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.

4. 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

5. There are several situations which can be mathematically represented by two equations that are not linear to start with. But we alter them so that they are reduced to a pair of linear equations.

**NCERT Book Solutions**

## Recent blog posts

- Latest at CBSE
- CBSE class X result has been declared on 24th May 2012
- CBSE results: Chennai zone rocks in Class 10 results
- CBSE Result 2012 for class 10
- CBSE Result 2012
- Important Notice : AIEEE 2012
- Vacancy Notice for CBSE Computer Assistant cum Clerk & Peon
- Important Procedure and Application Forms for India CBSE board, class x. class Xi, class Xii, Class 9
- Pre- Examination Highlights-2012
- Frequently Asked Questions on AIEEE 2012 Online Examination