NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables (Ex 3.1) Exercise 3.1

NCERT, or the National Council for Educational Research and Training, is an organisation that publishes a variety of educational materials to assist students and teachers in schools. It provides textbooks for all classes and all subjects. NCERT books are a part of the curriculum in many schools especially the ones affiliated with CBSE or Central Board of Secondary Education. These books published by the NCERT provide in-depth knowledge of all subjects and topics. The NCERT book for Mathematics is a great tool for students to understand how different types of questions must be solved. It provides students with examples to help students understand how the structure of the answer should be and what is the most appropriate method of structuring the solution. Method of the solution is an important aspect of writing answers in board examinations as it helps students increase their scores. Questions can be solved in different ways but not all of them might be considered correct by the instructor.

Hence it is important for students to use the correct method of solution which is acceptable to the board. The NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1 will help students to understand which method should be used for solving certain types of questions. The NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1 is a helpful tool for students. The NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1 can be of help to students of Class 10. The students of Class10 need to focus on the information given in the NCERT to score well in their examinations at the end of the term. Exercises in the NCERT textbook are meant to train students to be able to solve advanced-level problems. The NCERT books start educating students about the basics of a concept before moving on to the advanced problems pertaining to them.  The questions given in the NCERT will help students form the foundation of course material or the chapter to help students solve further problems. The NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1 will help students to solve their doubts about Exercise 3.1 Class 10 Maths in NCERT.

Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Exercise 3.1

The Class 10 Maths Ex 3.1 is part of Chapter 3 Pair Of Linear Equations In Two Variables. This chapter will help students understand the use of variables while solving a question and figuring out the answer to questions with two variables. These will help students to solve various numerical problems and it will also increase their scores in board examinations. This chapter will also aid students in understanding what the general form of a pair of linear equations is, how it can be represented, the graphical method of its solution, the algebraic method of solution and how the linear equations are identified depending on their terms. Students will be able to solve questions requiring a higher level of conceptual understanding. The NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1 could turn out to be a good first step to start their preparation. The NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1will be a helpful tool for students.

The NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1 include an overview of Chapter 3. The NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1 include topics such as the introduction to pair of linear equations in two variables, graphical method of solution of a pair of linear equations, algebraic methods of solution for a pair of linear equations, substitution method, elimination method, cross multiplication method and the solution of equations reducible to a pair of linear equations in two variables. The NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1 give solutions to the questions pertaining to these concepts which are also enclosed in Exercise 1 of Chapter 3. Students must understand these concepts to be able to solve advanced questions about similar concepts associated with the themes of linear equations and quadratic equations in the future. Studying this chapter thoroughly will help students in solving further exercises and questions. In addition to gaining advanced knowledge, it will enable them to solve questions that are perceived to be difficult. The NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1 will prove to be a valuable tool for students in achieving this goal.

Important Topics

Some of the topics included in the Class 10 Maths Chapter 3 Exercise 3.1 are the introduction to pairs of linear equations in two variables and how to interpret them. This exercise is meant to teach students how to form a linear equation with two variables. This exercise will also provide them with an understanding of how these equations are represented and integrated. However, as is evident from the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1, this chapter has various other important topics like using Algebraic Methods of Solution for Finding the Answer to Linear Equations in Two Variables. In this chapter, students learn about linear equations that will help them in higher classes and at more advanced levels.

The exercises that follow the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1 comprise some topics of priority that will help students to answer many different questions, whether basic or advanced. The NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1 will surely help students with the fundamentals of these concepts. Their performance and understanding will improve in later chapters. These topics are very important for students to understand if they wish to study Mathematics in-depth. The NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1 will be of great help to students if they feel stuck with any question. The NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1 will help them find answers to their queries and to find their lacunae and rectify them. Strengthening the concepts embedded in one part of the chapter will be helpful to students in solving further exercises and chapters as these formulas and concepts could have an application in them. The NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1 are a tool for students available on the website and Learning App of Extramarks for students to use.

Access NCERT Solutions for Class 10 Maths Chapter 3 – Pair of Linear Equations in Two Variables

The purpose of NCERT exercises is to assess how well students understand the concepts covered in a chapter. NCERT solutions are crucial for board examinations. Referring to the study materials for Mathematics Class 10 like the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1 on the Extramarks website and Learning App will be of help if students are having difficulty comprehending the Chapter 3 Pair of Linear Equations in Two Variables. If students find this chapter complex, they can turn to the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1, which offer solutions to any queries they may have. As the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1 are available to students online on the Extramarks platform, students can use it anytime to improve their academic performance and plan their examination preparation.

It is important for students to receive assistance when they feel stuck if they have recurring questions or doubts. When attempting to resolve a challenge in the course of study, teachers and peers may be helpful. Students can also alleviate their concerns by utilising the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1 and other tools made available on the Extramarks portal. In order to perform well on an examination later on and to be able to find solutions to questions that are similar to or the same as that question, students must be able to understand a question’s approach. The more quickly students can interpret a question and determine the technique of drafting a solution, the easier it will be for them to respond appropriately to a question during an examination. This is crucial to remember for each test they take. Therefore, in order to save time during examination preparation as well as on test day, it is imperative for students to consistently practice NCERT questions. They can obtain help with the same through the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1.

NCERT Solutions For Class 10 Chapter 3 Maths Exercise 3.1

The foundational concepts of Mathematics and other courses are primarily taught in schools using textbooks compiled by the NCERT. The Mathematics NCERT book is one of the suggested textbooks for board examinations. As a result of the centrality of the NCERT textbook, most students prioritise solving it before working on practice papers or taking a test. The NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1 will be helpful to students as they progress through the NCERT. They can utilise the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1 to quickly get accurate answers or efficient solutions to various problems. Through studying NCERT, students will acquire the skills to solve additional problems from other textbooks or to ace examinations to have their abilities evaluated and any shortcomings they have would be duly identified.

Students must remember what they have studied in the designated chapter through the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1. Students of Class 10 learn about the general form of a pair of linear equations. Students also learn how linear Equations can be represented through graphs and algebra. The graphical method of representation is done by drawing two lines representing the equations on a graph paper or Cartesian plane. Extensively, the nature of these lines and their interaction represents the nature of the solution for these equations. The nature of solutions for equations could be consistent or inconsistent depending on the nature of their graph. Moreover, there is a detailed discussion of algebraic methods for solving linear equations in detail.

Three algebraic methods of solution are mentioned in the chapter namely the substitution method, the elimination method and the cross multiplication method. In addition to the method of solution for a pair of linear equations, this chapter also helps students learn how to perceive a pair of linear equations and the nature of its solution algebraically. Three cases have been given in the chapter regarding the identification of which pairs of linear equations could be considered consistent or inconsistent. This chapter also educates about situations which can be mathematically represented through a graph or algebraically using linear equations at two variables. These situations may not be linear to start with but they can be reduced to a pair of linear equations by altering them.

It is possible for students to fill in the gaps in their skills and knowledge by repeatedly answering the questions and by using the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1. Students must seek assistance if they find a topic difficult, feel that their answer might be inaccurate, or believe that it will take too long to solve in the examination. Alternatively, it is noteworthy that the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1 can provide more effective answers to students. After completing the NCERT textbook, they will have a thorough understanding of the types of questions and concepts and how to respond to them.

Why Should You Get Class 10 Maths Ex 3.1 Solutions from Extramarks?

There are several benefits to referring to Extramarks for the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1, some of which are as follows:

• Extramarks’ study materials, which include the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1, are compiled by Extramarks Experts for facilitating efficacy in the learning of students. As a result, before being published online, these responses are evaluated for inconsistencies.
• Extramarks’ NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1 will provide an overview of the exercise and its contents along with providing students with comprehensive solutions.
• Using Extramarks’ NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1, students may learn about linear equations in two variables and understand how they are used.
• Due to its availability on both the website and the Learning App, Extramarks’ NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1 are accessible conveniently to students.
• The NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1 provide a precise method of solution with correct answers, a description of the processes used in the question, and details on how significant these steps are for board examination marks.

The NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1 are one of the many study materials that are available on Extramarks. Additionally, Extramarks provides NCERT Solutions, including NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1, for various levels of study. One such precise set of solutions provided by Extramarks is the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1.

NCERT Solutions for Class 10 Maths Chapter 3 Exercises

There are a lot of study materials available on the Extramarks educational website including the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1. Extramarks provides curated study material for other classes too. On the Extramarks learning portal, students can find NCERT Solutions for many classes and subjects of respective levels. The NCERT Solutions Class 12 and NCERT Solutions Class 11 are available for students for senior secondary classes. The NCERT Solutions Class 9 and NCERT Solutions Class 10 are available for students in secondary classes. For students in middle school, the NCERT Solutions Class 6, NCERT Solutions Class 7 and NCERT Solutions Class 8 are present on the website and mobile application of Extramarks. Students receiving primary education in schools could access NCERT Solutions Class 1, NCERT Solutions Class 2, NCERT Solutions Class 3, NCERT Solutions Class 4 and NCERT Solutions Class 5 for efficient learning.

Q.1 Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting?) Represent this situation algebraically and graphically.

Ans.
Let the present age of Aftab and his daughter be x years and y years respectively.
So, seven years ago,
Aftab’s age = (x–7) years and his daughter’s age = (y–7) years
According to the question,
x–7 = 7(y–7)
or x – 7y + 42 = 0
Three years hence,
Age of Aftab = (x + 3) years
Age of daughter = (y + 3) years
According to the question,
x + 3 = 3(y + 3)
or x – 3y – 6 = 0
Hence, the given information is represented algebraically by the two equations below.
x – 7y + 42 = 0
x – 3y – 6 = 0
To represent these equations graphically, we need at least two solutions for each equation. We write these solutions in table.
x – 7y + 42 = 0
or x = 7y – 42

 x 0 –7 7 y 6 5 7

Also,
x – 3y – 6 = 0
or x = 3y + 6

 x 0 –3 3 y –2 –3 –1

The graphical representation is given below.

Q.2 The coach of a cricket team buys 3 bats and 6 balls for ₹ 3900. Later, she buys another bat and 2 more balls of the same kind for ₹ 1300. Represent this situation algebraically and geometrically.

Ans.
Let the price of a bat and a ball be x and y respectively.
According to the question,
3x + 6y = 3900 …(1)
or 3 (x + 2y) = 3900
or x + 2y = 3900/3 =1300 …(2)
Equation (1) represents the total price of 3 bats and 6 balls whereas equation (2) represents the total price of one bat and 2 balls.
To represent these equations graphically, we need at least two solutions for each equation. We write these solutions in table.
3x + 6y = 3900
or y = (3900 – 3x)/6

 x 100 300 y 600 500

(i)
Also,
x + 2y =1300
or y = (1300 – x)/2

 x 500 900 y 400 200

(ii)
The below given graphical representation shows that
graphs of both the equations coincide.

Q.3 The cost of 2 kg of apples and 1 kg of grapes on a day was found to be ₹ 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is ₹ 300. Represent the situation algebraically and geometrically.

Ans.
Let the price of 1 kg of apple and 1 kg of grapes be ₹ x and ₹ y respectively.
According to the question,
2x + y = 160 …(1)
And
4x + 2y = 300
or 2x + y = 150 …(2)
Equations (1) and (2) represent the given situation algebraically.
To represent the given situation graphically, we need at least two solutions for each equation. We write these solutions in table.
2x + y = 160 …(1)
or y = 160 – 2x

 x 60 40 y = 160 – 2x 40 80

(i)
Also,
2x + y = 150 …(2)
or y = 150 – 2x

 x 60 40 y = 150 – 2x 30 70

(ii)
The graphical representation of the situation is given below. The two lines never intersect each other, i.e., the two lines are parallel.