## myCBSEguide App

CBSE, NCERT, JEE Main, NEET-UG, NDA, Exam Papers, Question Bank, NCERT Solutions, Exemplars, Revision Notes, Free Videos, MCQ Tests & more.

Install Now

CBSE class 10 Mathematics Chapter 3 Pair of Linear Equations in Two Variables notes in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Pair of Linear Equations in Two Variables class 10 Notes latest chapter wise notes for quick preparation of CBSE board exams and school based annual examinations. Class 10 Mathematics notes on Chapter 3 Pair of Linear Equations in Two Variables are also available for download in CBSE Guide website.

## CBSE Guide Pair of Linear Equations in Two Variables class 10 Notes

CBSE guide notes are the comprehensive notes which covers the latest syllabus of CBSE and NCERT. It includes all the topics given in NCERT class 10 Mathematics text book. Users can download CBSE guide quick revision notes from myCBSEguide mobile app and my CBSE guide website.

## 10 Mathematics notes Chapter 3 Pair of Linear Equations in Two Variables

Download CBSE class 10th revision notes for Chapter 3 Pair of Linear Equations in Two Variables in PDF format for free. Download revision notes for Pair of Linear Equations in Two Variables class 10 Notes and score high in exams. These are the Pair of Linear Equations in Two Variables class 10 Notes prepared by team of expert teachers. The revision notes help you revise the whole chapter in minutes. Revising notes in exam days is on of the the best tips recommended by teachers during exam days.

# Download Revision Notes as PDF

**CBSE Class–10 Mathematics Revision Notes**

**CHAPTER 03**

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

- Pair of Linear Equations in Two Variables
- Graphical Method of Solution
- Algebraic Methods of Solution
- Substitution Method
- Elimination Method
- Cross-Multiplication Method
- Equations Reducible to a Pair of Linear Equations

1. A pair of linear equations in two variables is said to form a system of simultaneous linear equations in two variables.

The most general form of a pair of linear equations is :

Where

are real numbers and,

- The solution of a linear equation is a pair of values, one for x and one for y. This pair of values is called
**Ordered pair**. - A pair of values of x and y satisfying each of the equations in the given system of two simultaneous equations in x and y is called a
**solution of the system**. - A pair of linear equations will have either (a)
**a unique solution**or (b)**infinitely****many solutions**or (c)**no solution**.

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

(i) If the lines intersect at a point, the pair of equations is consistent.The point of intersection gives the unique solution of the equations.

(ii) If the lines coincide, then there are infinitely many solutions. The pair of equations is consistent. Each point on the line will be a solution.

(iii) If the lines are parallel, the pair of the linear equations has no solution. The pair of linear equations is inconsistent.

Thus, corresponding to each solution (x, y) of the linear equation ax + by + c = 0, there exists a point on the line representing the equation ax + by + c = 0 and vice versa.

3. If a pair of linear equations is given by

and(i)

the pair of linear equations is consistent. (Unique solution).(ii)

the pair of linear equations is inconsistent(No solution).(iii)

the pair of linear equations is dependent and consistent (infinitely many solutions).4. **Solution of pairs of linear equations in two variables algebraically**:

Solution by **Substitution method**:

Let the pair of equations be

and- From one of the equations, express one of the variables say y in terms of the other variable i.e., x.
- Substitute the value of y, obtained in above step, in other equation, the getting an equation in x.
- Solve the equation and get the value of x.
- Sustitute the value of x in expression for y obtained in first step and get the value of y.

Solution by **Elimination method**, i.e., by **equating the coefficients**:

- in the two given equations, make the coefficients of one of the variables numerically equal. To do so, multiply these coefficients by suitable constant.
- Add or subtract the equations obtained in above step according as the terms having same coefficients are of the opposite or of the same signs and get an equation in only one variable.
- Solve the equation found and get the value of one of the variable.
- Sustitute the value of this variable in either of the two given equations and find the value of the other variable.

Solution by **Cross Multiplication method**:

Let the pair of equations be

andTo find the values of x and y, we have the formulae:

and

## Pair of Linear Equations in Two Variables class 10 Notes

- CBSE Revision notes (PDF Download) Free
- CBSE Revision notes for Class 10 Mathematics PDF
- CBSE Revision notes Class 10 Mathematics – CBSE
- CBSE Revisions notes and Key Points Class 10 Mathematics
- Summary of the NCERT books all chapters in Mathematics class 10
- Short notes for CBSE class 10th Mathematics
- Key notes and chapter summary of Mathematics class 10
- Quick revision notes for CBSE board exams

**CBSE Class-10 Revision Notes and Key Points**

Pair of Linear Equations in Two Variables class 10 Notes. CBSE quick revision note for Class-10 Mathematics, Chemistry, Maths, Biology and other subject are very helpful to revise the whole syllabus during exam days. The revision notes covers all important formulas and concepts given in the chapter. Even if you wish to have an overview of a chapter, quick revision notes are here to do if for you. These notes will certainly save your time during stressful exam days.

- Revision Notes for class-10 Mathematics
- Revision Notes for class-10 Science
- Revision Notes for class-10 Social Science
- Revision Notes for class-10 English Communicative

To download Pair of Linear Equations in Two Variables class 10 Notes, sample paper for class 10 Mathematics, Social Science, Science, English Communicative; do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through **the best app for CBSE students** and myCBSEguide website.

- Real Numbers class 10 Notes Mathematics
- Polynomials class 10 Notes Mathematics
- Pair of Linear Equations in Two Variables class 10 Notes Mathematics
- Quadratic Equations class 10 Notes Mathematics
- Arithmetic Progressions class 10 Notes Mathematics
- Triangles class 10 Notes Mathematics
- Coordinate Geometry class 10 Notes Mathematics
- Introduction to Trigonometry class 10 Notes Mathematics
- Some Applications of Trigonometry class 10 Notes Mathematics
- Circles class 10 Notes Mathematics
- Constructions class 10 Notes Mathematics
- Area Related to Circles class 10 Notes Mathematics
- Surface Areas and Volumes class 10 Notes Mathematic
- Statistics class 10 Notes Mathematics
- Probability class 10 Notes Mathematics