Class 10 Maths NCERT Revision Notes Ch 3 | NCERT Class 10

Class 10 Maths Chapter 3 Overview

The Chapter, Linear Equations In Two Variables, is all about linear equations that have two variables such as x + y = 1.

We will learn how to plot graphs of linear equations and find their solutions graphically.

In this chapter, we are going to study a lot about liner equations and methods to find their zeroes.

In this chapter, we have to study various methods used by mathematicians to find zeroes of linear equations having two variables such as substitution method, elimination method, and cross multiplication method.

In this chapter, we will study about consistent and inconsistent linear equations also.

Class 10 Maths Notes of Chapter 3 Pair of Linear Equations In Two Variables

1. Linear Equation

An equation in which the highest degree of the variable is one is called a linear equation.

2. Linear Equations In Two Variables

The linear equation having two variables is known as a linear equation in two variables.

3. Graph of A Linear Equation In One Variables

The graph of a linear equation in one variable is always a point.

4. Graph of A Linear Equation In Two Variables

The graph of a linear equation in two variables is always a straight line.

5. System of Equations

When dealing with two equations simultaneously, it is known as a system of equations.

6. Types of solutions of the system of equations

(i) No Solution: a₁/a₂ = b₁/b₂ not= c₁/c₂

(ii) Unique Solution: a₁/a₂ not= b₁/b₂

(iii) Infinitely Many Solutions: a₁/a₂ = b₁/b₂ = c₁/c₂

7. Graphs of System of Linear Equations

(i)Graph of no solution has parallel lines

(ii) graph of a unique solution have intersecting lines

(iii) graph of infinitely many solutions have coincident lines.

8. Consistent System of Equations

A consistent system refers to the system of equations having at least one solution.

9. Inconsistent System of Equations

The inconsistent system refers to the system of the equation has no solution.

10. System of Simultaneous Equations

A system of simultaneous equations is said to be homogenous if all of the constant terms are zero.
General form = a₁x + b₁y = 0 and a₂x + b₂y = 0
Homogeneous equation of the form ax + by = 0 is a line passing through the origin(0,0).

12. Methods To Solve Linear Equations

• Elimination Method.
• Substituion Method.
• Cross Multiplication method.

11. Cross Multiplication Method

In cross multiplication method, we use the given formula

With the use of the above formula we can solve linear equations in two variables very easily by just putting the values from the equations in this formula.

Conclusoin

Maths is a bery simple subject if you practice it fon daily basis.

I hope you love reading the notes on "Class 10 Maths Revision Notes Ch 3 Pair of Linear Equations In Two Variables".