# NCERT Solutions for Class 9 Maths Chapter 4- Linear Equations In Two Variables Exercise 4.3

Mathematics helps students build analytical thinking and reasoning abilities. They become capable of approaching life problems in a logical way. It enables students to make the right decisions in their lives. It is one of the important skills that students need to learn in primary classes. Mathematics is applied in various fields such as Physics, Chemistry, Economics, Social Science, etc. It is one of the subjects that has extensive applications in so many fields, and it must be well focused on by students. All the subjects in Class 9 are useful for learning topics in Class 10. It provides a base for topics that will be covered in Class 10, so students must focus well on studying subjects that are included in the Class 9 curriculum. It has become important to make use of online learning materials to prepare effectively for examinations. Online learning enables students to study according to their own schedules. They can download lectures and study whenever it is convenient for them. Students can also study according to their own learning styles with the assistance of online learning platforms. Study materials available online are designed in different media that allow students to learn according to their own learning styles. There are various online learning platforms for students to choose from. Students should be careful about choosing online learning platforms. Extramarks is a very trustworthy learning portal, and it is trusted by the vast majority of students in India.

Students having difficulties solving exercises in Chapter 4 can refer to the NCERT solutions provided by Extramarks. All the topics of Chapter 4 are important from the examination perspective and students need to focus well while going through the chapter. It is important to learn the theoretical part of Chapter 4 in a comprehensive manner. Students are advised to revise the topics regularly so that they are retained for a longer time in their minds. Chapter 4 in Class 9 Mathematics consists of 4 exercises. All the exercises are useful for scoring well in the mathematics examination. Students should practice each one of the exercises to improve their mathematics exam preparation. Class 9 students can easily solve Exercise 4.3 with the assistance of the NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3. The NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3, are available on the Extramarks learning portal in PDF format.

It is important to solve past years’ papers regularly. Students should solve previous year’s papers under time constraints and in an exam setting.  Solving past years’ papers will help students understand the distribution of marks in Mathematics. Practising questions according to the marks distribution helps in scoring higher marks in the examination. Past years’ papers are also useful for knowing the paper pattern of Mathematics. Class 9 students can access past years’ papers of Mathematics from the Extramarks website and mobile application. The past years’ papers available on Extramarks are free of any errors. Students can also download solutions of past years’ papers from Extramarks.

Theoretical concepts in a subject like Mathematics must be studied daily by students. Since questions from every chapter are covered in the Mathematics examination, it is crucial for students to pay equal attention to each chapter. These chapters must be reviewed from time to time.

Each topic in the mathematics textbook is explained with the aid of solved examples. For ease of comprehension, each solved example is typically accompanied by a step-by-step guide. To better comprehend the topics, students should read through the examples provided in the textbook. Students usually forget to solve all the exercise questions. By practising the exercises, students gain a better understanding of the concepts and are better prepared for the examinations. In order to score higher in the mathematics examination, students must develop the habit of solving exercise questions. The NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3, are beneficial in developing the habit of regularly practising exercise questions.

Mathematics is a crucial subject in the Class 9 curriculum. Many students find it difficult to practice mathematical concepts. It is critical to use online resources to prepare well for the mathematics examination. While reading the NCERT textbooks, it is necessary to focus on the topics. To build confidence, all Class 9 students are advised to continue practising the exercise questions from the Mathematics chapters. Students can use the NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3, to boost their confidence when practising exercise questions. The NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3, can help them understand all of the important formulae and equations of the Graph of a Linear Equation in Two Variables topic. Study materials like the NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3, are very beneficial for improving the knowledge of students.

The NCERT solutions are very important study materials that are significant for improving performance in Mathematics examinations. Class 9 students can access NCERT solutions for all the subjects in their course with the help of Extramarks. To prepare for the Mathematics examination, the NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3, are very essential. Students can trust their authenticity, as expert Mathematics teachers have designed them. Students can improve their learning experience under the guidance of Extramarks. All of the study materials required for obtaining higher marks in examinations are made available on the Extramarks website and mobile application. On Extramarks, students can attend live lectures for all subjects. The live lectures are delivered by expert teachers from India, and students from all backgrounds can benefit from them. Extramarks assists students in overcoming doubts and confusions that arise during exam preparation. Students can learn the fundamentals of Mathematics by reading NCERT textbooks. After learning the fundamentals, it is critical to solve the practice problems provided between chapters. Students who are having difficulty solving the questions in Exercise 4.3 can make use of the NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3.

It is critical to identify students’ weak areas in a subject. A thorough revision and practice are helpful in understanding the weaker sections of Class 9 Mathematics. Students are required to focus more on practising questions related to topics that are difficult. They can solve all the difficult problems related to the Graph of a Linear Equation in Two Variables topic by utilising the NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3. The NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3 are accessible on the Extramarks learning portal.

The National Council of Educational Research and Training is an autonomous organisation set up by the government of India. It is responsible for advising and assisting the state and central governments to bring improvements to school education. The NCERT has the right to publish the textbooks for the CBSE Board curriculum. All the textbooks from NCERT are very affordable and easy to understand. The NCERT is also in charge of conducting research in the sphere of school education. The research conducted by NCERT is helpful in improving the learning experience of students. The innovations and ideas suggested by the NCERT are mandated in every school in India. NCERT also plays a vital role in supervising the training of teachers at the secondary and primary school levels. There are many functional units of NCERT scattered around different parts of India to facilitate the proper workings of the organisation.

Students should revise the topics again and again for more clarity. Revision helps in solving questions given in the exercises. They are supposed to keep referring to the revision notes provided by Extramarks to quickly revise the important topics in Mathematics. They can download the revision notes for Mathematics from Extramarks. All the topics of Chapter 4 are necessary for improving the preparation of Class 9 students. The NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3, are available in PDF format. Students can take the help of the NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3, to learn to solve questions in a stepwise manner. Students will learn to solve questions in logically correct steps by referring to these solutions. All the formulae and derivations should be revised periodically to get the desired solutions to questions related to Chapter 4. The NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3, are helpful in revising the formulae and derivations of the chapter. Exercise 4.3 is based on the topic Graph of a Linear Equation in Two Variables. Students should pay attention to the graphs given under the topic. They should draw graphs while solving questions as well. The NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3 are beneficial for solving questions along with graphical representations. Students of Class 9 are advised to access the NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3, from the Extramarks website and mobile application. All the questions of Exercise 4.3 can be practised with the help of the NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3.

Some questions in Exercise 4.3 Class 9 Maths can seem complex for students to solve. Students will learn to break down complex questions into smaller steps with the help of the NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3. It is recommended for students to keep referring to the NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3 whenever they get confused while solving Exercise 4.3. Problem-solving skills are necessary for practising questions in Mathematics. Class 9 students can learn better problem-solving skills by using the NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3. Each solution is given in a detailed manner. In order to solve questions effectively, students must make use of the NCERT solutions. All the solutions are given in a well-structured format. Practising questions is crucial for improving the calculation speed of students. The NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3, enable students to solve questions easily. Extramarks has all the study materials available that are essential for boosting the performance of students in the Mathematics examination. Students must keep referring to the study materials on a regular basis to score higher marks in the examination.

Students are encouraged to refer to the solved examples given in Chapter 4. Solved examples are very helpful in understanding the methods of solving problems and the kind of questions that can be framed from the topics. Each of the solved problems is given in a well-structured manner in the NCERT textbook. Students are advised to go through them one by one. The examination consists of questions that can take a lot of time to solve. It becomes necessary for students to manage time while solving questions. Students must learn time management skills in order to solve the question paper of Mathematics within the allotted time. Practising questions with the help of the NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3 is beneficial for learning better time management skills.

## NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables (Ex 4.3) Exercise 4.3

Students may have difficulties finding the appropriate NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3. The Extramarks learning platform provides very exact NCERT solutions for all the chapters of each subject. The NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3, are easily accessible on Extramarks in PDF format. Students can enhance their learning process with the aid of the NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3. Students are advised to keep assessing their examination preparation in order to bring necessary improvements in the learning strategy. Consistent practice and revision are helpful in getting self-assessment for Mathematics examination preparation. Referring to the NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3, is useful for students to make important changes in their methods of practising. All the Class 9 Maths Chapter 4 Exercise 4.3 Solutions are available in PDF format.

### Access NCERT Solutions for Maths Chapter 4 – Linear Equations in two Variable

Students must access the NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3, from the Extramarks website and mobile application. They can also access the NCERT solutions for other exercises of Chapter 4 and other chapters in the syllabus. Before answering questions, students must understand their prerequisites. The NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3, are helpful in knowing the requirements of questions so that they can be solved effectively.

### EXERCISE 4.3

There are 8 questions in Class 9 Maths Chapter 4 Exercise 4.3, and a few of them are based on the graphs. Students are required to revise the theory of the Graph of a Linear Equation in Two Variables topic to be able to solve the questions in Exercise 4.3. Students must compare their solutions with the NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3, to make any required adjustments. The Class 9 Maths Exercise 4.3 Solution are important for improving the performance of students in Mathematics. They are required to keep practising the exercises in Chapter 4 to enhance their ongoing preparation for the Mathematics examination. Extramarks’ learning platform can assist students in looking for authentic and reliable study resources for the Mathematics exam. All of the resources available on the Extramarks website and mobile application help students improve their learning capacity. Extramarks can assist students in effectively preparing for various competitive examinations such as JEE, NEET, CUET, and others. Students must set personal goals for themselves and work to achieve them within the time frame provided. Examination results are critical in determining a student’s potential.

### NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables Exercise 4.3

The derivations are essential for understanding Mathematical topics. Students should concentrate on learning the Probability chapter’s derivations to improve their understanding of the concepts. Focusing on the derivations helps students retain formulas in their memory for a longer period of time when practising exercise questions. The NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3, make it simple to review the derivations given in the Graph of a Linear Equation in Two Variables topic. The majority of the chapters in Mathematics are built on previous chapters. As a result, when beginning to prepare new chapters in Mathematics, it is necessary to recall concepts from past classes. Students must set goals for themselves and strive to achieve them within the time frame provided. Examinations are very important in determining a student’s ability. Each test helps students improve their knowledge of a subject. Mathematics at the Class 9 level consists of important topics that must be reviewed repeatedly. Students must concentrate on learning each topic from the standpoint of the exam. Students can give mock tests to assess their understanding of a specific chapter. Class 9 students can take various Mathematics mock tests on the Extramarks website and mobile application. These mock tests are beneficial in building students’ confidence for the upcoming Mathematics examination.

### NCERT Solutions for Class 9

NCERT solutions are available for each subject of Class 9. Students can download them exercise-wise from Extramarks. The NCERT solutions are curated by the best teachers of each subject and Class 9 students will be able to score well in their examinations. All the NCERT solutions are very authentic and easy to comprehend.

### CBSE Study Materials for Class 9

Class 9 students can refer to the study materials available on Extramarks to solve their doubts and confusion related to the subjects in their course. All the study materials are easily accessible on the Extramarks website and mobile application. They should refer to them consistently. Extramarks has live class programmes that use conventional and new-age learning methodologies for building the concepts of a chapter. CBSE students of all classes can get reliable and authentic study materials from Extramarks.

### CBSE Study Materials

Extramarks provides study materials for all the subjects on the CBSE Board. They are prepared according to the latest CBSE syllabus so that students can fully benefit from them. CBSE students can access NCERT solutions, past years’ papers, sample papers, revision notes, etc. from the Extramarks learning platform. All these study resources are beneficial for increasing the understanding of students so that they can score higher marks in their examinations. Every student has a distinct learning style. Some students may not receive adequate guidance in the classroom. They are advised to prepare for their exams by using online resources that suit their learning style. They must obtain study materials from reputable sources to ensure that their exam preparation is on track. They can also improve their self-study by using online resources. It is true that internet learning resources cannot completely replace traditional learning methods, but it is necessary to combine traditional methods with modern methods for effective learning. Students from all socioeconomic backgrounds can now easily access study resources thanks to advances in technology and the internet. Combining traditional teaching methods with online techniques can provide students with new learning opportunities. Students from outlying areas can benefit from the use of online learning platforms as well.

Q.1 Draw the graph of each of the following linear equations in two variables:
(i) x + y = 4
(ii) x – y = 2
(iii) y = 3x
(iv) 3 = 2x + y

Ans

(i) Graph of x + y = 4 is given below:

(ii) Graph of x – y = 2 is given below:

(iii) Graph of y = 3x is given below:

(iv) Graph of 3 = 2x + y is given below:

Q.2 Give the equations of two lines passing through (2, 14). How many more such lines are there, and why?

Ans
The point (2, 14) satisfies the equations x + y = 16 and y – x = 12.
Therefore, x + y = 16 and y – x = 12 are the two lines passing through the point (2, 14).
Since, infinite number of lines can pass through one point, therefore, there are infinite lines of such type passing through the given point (2, 14).

Q.3 If the point (3, 4) lies on the graph of the equation 3y = ax + 7, find the value of a.

Ans
Since, the point (3, 4) lies on the graph of the equation 3y = ax + 7, so it will satisfy the equation.
Putting x = 3 and y = 4 in given equation, we get
3(4) = a(3) + 7
12 = 3a + 7
5 = 3a
a = (5/3)

Q.4 The taxi fare in a city is as follows: For the first kilometre, the fare is Rs 8 and for the subsequent distance it is Rs 5 per km. Taking the distance covered as x km and total fare as Rs y, write a linear equation for this information, and draw its graph.

Ans
Total covered distance = x km
Fare of first km distance = Rs. 8
Fare of the fare rest distance = (x – 1)5
Total fare of x km distance = 8 + (x – 1)5
y = 3 + 5x
or 5x – y + 3 = 0
which is the linear equation of the given informations.

 x 0 –(3/5) y 3 0

The graph of 5x – y + 3 = 0 is given below:

Q.5 From the choices given below, choose the equation whose graphs are given in Fig. 4.6 and Fig. 4.7.
For Fig. 4. 6 For Fig. 4.7
(i) y = x (i) y = x + 2
(ii) x + y = 0 (ii) y = x – 2
(iii) y = 2x (iii) y = –x + 2
(iv) 2 + 3y = 7x (iv) x + 2y = 6

Ans
(i) Points on the given line are (−1, 1), (0, 0), and (1, −1).
We see that these points satisfies equation
x + y = 0. So, x + y =0 is the required equation of the given graph.
Hence, the correct answer is (ii) x + y = 0. (ii) Since, points on the given line are (−1, 3), (0, 2), and (2, 0). We see that these points satisfies equation y = – x + 2. So, y = – x + 2 is the required equation of the given graph.
Therefore, the correct answer (iii) y = – x + 2.

Q.6 If the work done by a body on application of a constant force is directly proportional to the distance travelled by the body, express this in the form of an equation in two variables and draw the graph of the same by taking the constant force as 5 units. Also read from the graph the work done when the distance travelled by the body is
(i) 2 units (ii) 0 unit

Ans

$\begin{array}{l}\text{Let the distance travelled and the work done by the}\mathrm{}\text{body be x}\\ \text{and y respectively}.\\ \text{Work done}\mathrm{}\text{\hspace{0.17em}}\mathrm{\alpha }\text{\hspace{0.17em}\hspace{0.17em}distance travelled}\\ ⇒\text{y}\mathrm{\alpha }\text{\hspace{0.17em}x}\\ ⇒\text{y}=\text{kx}\mathrm{},\text{where k is constant.}\\ \mathrm{If}\text{contant force is 5 units, then work done}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}y}=5\mathrm{x}\\ \begin{array}{}\end{array}\end{array}$

 x 0 2 –2 y 0 10 –10

(i) From the graphs, it can be observed that the value of y corresponding to x = 2 is 10. This implies that the work done by the body is 10 units when the distance travelled by it is 2 units. (ii) From the graphs, it can be observed that the value of y corresponding to x = 0 is 0. This implies that the work done by the body is 0 units when the distance travelled by it is 0 unit.

Q.7 Yamini and Fatima, two students of Class IX of a school, together contributed Rs 100 towards the Prime Minister’s Relief Fund to help the earthquake victims. Write a linear equation which satisfies this data. (You may take their contributions as Rs x and Rs y.). Draw the graph of the same.

Ans
Let money donated by Yamini = Rs. x
And money donated by Fatima = Rs. y
Total contributed money = Rs. 100
Then, x + y = 100
The graph of linear equation x + y = 100 is:

Q.8 In countries like USA and Canada, temperature is measured in Fahrenheit, whereas in countries like India, it is measured in Celsius.
Here is a linear equation that converts Fahrenheit to Celsius:
F = (9/5) C + 32
(i) Draw the graph of the linear equation above using Celsius for x-axis and Fahrenheit for y-axis.
(ii) If the temperature is 30°C, what is the temperature in Fahrenheit?
(iii) If the temperature is 95°F, what is the temperature in Celsius?
(iv) If the temperature is 0°C, what is the temperature in Fahrenheit and if the temperature is 0°F, what is the temperature in Celsius?
(v) Is there a temperature which is numerically the same in both Fahrenheit and Celsius? If yes, find it.

Ans
(i) The given equation is: F = (9/5) C + 32
Let degree Celsius are taken on x-axis and Fahrenheit is taken on y- axis.
Then equation becomes:
y = (9/5) x + 32

 x 0 10 –10 y 32 50 14

The graph of the above equation is constructed as given below:

(ii) Temperature at 30°C
F = (9/5)30°C + 32
= 86
Therefore, temperature in Fahrenheit is 86°F. (iii) Temperature = 95°F
95 = (9/5) C + 32
63 = (9/5) C
C = 63 × (5/9) = 35°
(iv) F = (9/5) C + 32
If C = 0°C, then
F = (9/5)(0) + 32
= 32
If F = 0, then
0 = (9/5) C + 32
–32 = (9/5) C
C = –32 x (5/9)
=–17.77
Therefore, if F = 0°F, then C = –17.77° C.
(v) F = (9/5) C + 32
If F = C, then
F = (9/5)F + 32
(1 – 9/5)F = 32
–(4/5)F = 32
F = 32 × (–5/4)
= – 40
Yes, there is a temperature, −40°, which is numerically the same in both Fahrenheit and Celsius.

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### 1. Where can a student get access to the NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3?

Students of Class 9 CBSE Board can access the NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3 from the Extramarks website and mobile application. The NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3 are beneficial for enhancing the Mathematics exam preparation of students. They can get solutions to all the questions of Chapter 4 Exercise 4.3 with the help of the NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3.

### 2. What are the topics and subtopics covered in Class 9 Mathematics?

The students are advised to refer to the latest syllabus of Class 9 Mathematics in order to know the topics and subtopics covered in Mathematics. Students can easily access the Mathematics syllabus from Extramarks. It can also be downloaded from the official website of NCERT.

### 3. Are the NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3 accessible in PDF format?

Class 9 students of the Central Board of Secondary Education can download the NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3 from the Extramarks website and mobile application in PDF format. Students can make use of the NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3 in offline mode as well, without having to worry about an internet connection.

### 4. What are the benefits of referring to the NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3?

The NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3 are helpful in boosting the ongoing preparation for the Mathematics exam. Students can score well in Mathematics with the help of the NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3. Class 9 students can get easy solutions to problems of Exercise 4.3 of Chapter 4 by utilising the NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3. Students are able to learn the best methods of solving exercise problems by using the NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3. The NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3 are beneficial for revising the concepts, formulae, theorems, etc related to each of the questions.

### 5. Are the NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3 available on Extramarks reliable?

The NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3 are prepared by expert Mathematics teachers. Each of the NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3 is given in a simple and easy-to-understand format. Students can rely on the NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3 to get better results in the Mathematics examination.

### 6. How can students of Class 9 score higher marks in the Mathematics examination?

Students need to practice the exercise question on a regular basis to understand the theories of chapters in depth. It is important to revise the definitions consistently. To score well in the Mathematics examination, students should keep referring to online resources from time to time. It is advisable to practice the sample papers and past years’ papers to get an idea of questions that can appear in the Mathematics examination. The NCERT Solutions For Class 9 Maths Chapter 4 Exercise 4.3 should be used to enhance the problem-solving skills of students.