NCERT Maths Chapter 3 Pair of Linear Equations in Two Variables

Pair of Linear Equations in Two Variables is an important chapter in NCERT Maths that deals with solving two linear equations containing two variables. These equations help represent and solve many real-life problems involving relationships between two quantities.

This chapter is important for CBSE Board Exams and Competitive Exams.

What is a Pair of Linear Equations?

A pair of linear equations in two variables can be represented as:

a?x + b?y + c? = 0

where x and y are variables and a, b, c are constants.

Methods of Solving Linear Equations

Graphical Method

In this method, the equations are represented as straight lines on a graph. The point where the two lines intersect gives the solution.

Substitution Method

One variable is expressed in terms of the other and substituted into the second equation to find the solution.

Elimination Method

One variable is eliminated by adding or subtracting the equations, making it easier to solve for the remaining variable.

Cross Multiplication Method

This method provides a direct formula-based approach to find the values of both variables.

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Types of Solutions

Unique Solution

When two lines intersect at one point.

No Solution

When two lines are parallel and never intersect.

Infinitely Many Solutions

When both equations represent the same line.

Applications of Linear Equations

Pair of linear equations are used in:

Age-related problems
Speed and distance problems
Cost and profit calculations
Mixture and investment problems

Importance of the Chapter

Develops logical and analytical thinking.
Forms the foundation for coordinate geometry.
Helps solve practical real-life problems.
Essential for higher mathematics.

Importance for CBSE Exams

This chapter is frequently tested in CBSE examinations. Students should practice solving equations using all methods and understand the conditions for different types of solutions.

Key Topics Covered

Pair of Linear Equations in Two Variables
Graphical Method
Substitution Method
Elimination Method
Cross Multiplication Method
Consistency of Equations
Unique Solution
No Solution
Infinitely Many Solutions
Real-Life Applications of Linear Equations

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