NCERT Solutions for Class 10 Maths Chapter 3 Exercise 3.1 Pair of Linear Equations in Two Variables - PDF Download

NCERT solutions for class 10 maths chapter 3 Pair of Linear Equations in two Variables ex 3.1 based on graphical and algebraic representations of linear equations. Students are able to comprehend the analytical meaning of a solution to a problem and find results from it.

This exercise will also assist students in revisiting the three possible outcomes when two lines are placed in the plane. three possible outcomes are: i) two lines intersect, ii) two lines do not intersect {parallel],  and iii) two lines intersect coincidently. All three outcomes are represented graphically and in an algebraic form. In order to perform the graphical plotting, you must determine the value of both variables. You can also check the consistency of equations graphically. 

The NCERT solutions are available for download. Class 10 maths ex 3.1 PDF can be downloaded for free from eSaral official website. Our subject experts have made this NCERT exercise 3.1 for class 10 maths so that students can understand the problem solving techniques of linear equations.

Topics Covered in Exercise 3.1 Class 10 Mathematics Questions

Chapter 3 ex 3.1 of class 10 maths includes the following topics:

1. Graphical Method of Solution of a Pair of Linear Equations - Linear equation is a system of two or more intersecting lines. The graph of the linear equation is just a line.b There are several ways of solving two linear equations, such as Substitution method, Elimination method, etc. Linear equations can also be solved by graphical methods, where we plot the graph of equations and attempt to find the intersection point.

Graphical Method of Solution - We can now summarize the behavior of lines representing a pair of linear equations in two variables and the existence of solutions as follows:

• Unique solution

• No Solution

• Infinitely Many Solutions

1. Unique solution - A linear equation in two variables that has a solution is called a "consistent pair of linear equations. In this case, both lines intersect each other.

2. No Solution - A pair of linear equations in two variables that don't have a solution are called an inconsistent pair of linear equations. In this case, both lines are parallel, meaning they don't intersect.

3. Infinitely Many Solutions - Linear equations in two variables that have an infinite number of solutions are called dependent pair linear equations. In this case, both the lines coincide with each other. 

Tips for Solving Exercise 3.1 Class 10 Chapter 3 Pair of Linear Equations in Two Variables

NCERT solutions Class 10 maths Chapter 3 ex 3.1 is a series of questions to test your knowledge of the fundamental concepts of linear equations in 2 variables. Here are a few important tips to solve ex 3.1. 

1. Exercise 3.1 of NCERT solutions class 10 maths chapter 3 Pairs of Linear Equations in two variables includes practical questions that students must practice as they introduce graphical and algebraic methods to find solutions of linear equations.

2. Through this exercise, students will find that there is an infinite number of solutions for a pair of linear equations.

3. NCERT solutions for class 10 maths chapter 3 ex 3.1 has a straightforward problem format that elucidates all the concepts graphically. This will enable the students to visualize linear equations and recognize the lines that represent each of these equations. Furthermore, they will be able to identify the type of equations by studying the graph.
   

Importance of Solving Ex 3.1 Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables

Here are some benefits of solving ex 3.1 class 10 maths chapter 3  Pair of Linear Equations in Two Variables.

1. chapter 3. ex 3.1class 10 maths is considered to be the best material to solve and revise all of the questions in this exercise and also helps us to understand the pair linear equations in two variables better.

2. You can gain practice by solving all the graphically represented linear equations in 2 variables in NCERT solution class 10th maths chapter 3 exam 3.1, and gain general knowledge about the topic. We can get higher marks in the exam by practicing thoroughly.

3. In Maths Class 10 ex 3.1, you'll need to understand the basics of how linear equations are represented graphically and in an algebraic way in two variables. You'll also need to understand the different kinds of solutions and how they're represented graphically, which are important concepts in this chapter.

4. The solutions will help the students do well in the exam.

Frequently Asked Questions

Question 1. When two lines are placed in a plane, what are the three possibilities ? 

Answer 1. The three possibilities are:

1. In some cases, two lines may intersect each other.

2. In some cases, they may not intersect, and may be parallel to each other.

3. Sometimes two lines may be coincident.

Question 2. How many solutions for a linear equation in two variables are there if the linear equations are consistent and dependent ?

Answer 2. Linear equations in two variables have an infinite number of solutions if the equations are consistent and dependent.

Question 3. What is the number of quadrants in a graph ?

Answer 3. There are four quadrants in a graph.