class 9 maths chapter 4 assignment

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

NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables are provided here. Our NCERT Maths solutions contain all the questions of the NCERT textbook that are solved and explained beautifully. Here you will get complete NCERT Solutions for Class 9 Maths Chapter 4 all exercises Exercise in one place. These solutions are prepared by the subject experts and as per the latest NCERT syllabus and guidelines. CBSE Class 9 Students who wish to score good marks in the maths exam must practice these questions regularly.

Class 9 Maths Chapter 4 Linear Equations in Two Variables NCERT Solutions

Below we have provided the solutions of each exercise of the chapter. Go through the links to access the solutions of exercises you want. You should also check out our NCERT Class 9 Solutions for other subjects to score good marks in the exams.

NCERT Solutions for Class 9 Maths Chapter 4 Exercise 4.1

NCERT Solutions for Class 9 Maths Chapter 4 Exercise 4.2

NCERT Solutions for Class 9 Maths Chapter 4 Exercise 4.3

NCERT Solutions for Class 9 Maths Chapter 4 Exercise 4.4

NCERT Solutions for Class 9 Maths Chapter 4 – Topic Discussion

Below we have listed the topics that have been discussed in this chapter.

In this chapter, the knowledge of linear equations in one variable is recalled and extended to that of two variables. Any equation which can be put in the form ax + by + c = 0, where a, b and c are real numbers, and a and b are not both zero, is called a linear equation in two variables.

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

Ncert solutions for class 9 maths chapter 4 linear equations in two variables| pdf download.

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

• Exercise 4.1 Chapter 4 Class 9 Maths NCERT Solutions
• Exercise 4.2 Chapter 4 Class 9 Maths NCERT Solutions
• Exercise 4.3 Chapter 4 Class 9 Maths NCERT Solutions
• Exercise 4.4 Chapter 4 Class 9 Maths NCERT Solutions

NCERT Solutions for Class 9 Maths Chapters:

How many exercises in chapter 4 linear equations in two variables , what do you mean by solution of a linear equation in two variables, what is the equation of x-axis, show that x = 1, y = 3 satisfy the linear equation 3x – 4y + 9 = 0., contact form.

NCERT Solutions for Class 9 Maths Chapter 4 Exercise 4.4

Ncert solutions for class 9 maths chapter 4 linear equations in two variables ex 4.4 – free pdf.

Free PDF of NCERT Solutions for Class 9 Maths Chapter 4 Exercise 4.4 prepared by expert Mathematics teacher at Mathongo.com as per CBSE (NCERT) books guidelines. Download our Class 9 Maths Chapter 4 Linear Equations in Two Variables Ex 4.4 questions with solutions to help you to revise complete syllabus and score more marks in your exams.

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NCERT Solutions for Class 9 Maths Chapter 4 Exercise 4.1

NCERT Solutions for Class 9 Maths Exercise 4.1 Linear equations in two variables in Hindi and English Medium for session 2024-25. Questions of 9th Maths ex. 4.1 are updated as per new textbooks following the revised syllabus for CBSE 2024-25.

Class 9 Maths Exercise 4.1 NCERT Solutions

• Class 9 Maths Exercise 4.1 in English
• Class 9 Maths Exercise 4.1 in Hindi
• Class 9 Maths Chapter 4 in PDF
• 9th Maths Chapter 4 Solutions
• Class 9 Maths NCERT Solutions
• Class 9 all Subjects NCERT Solutions

If you have studied the linear equations in the previous class you can recognize now the single variable linear equations. Learn here about the basic difference between expression and equation. Similarly, two variables equations will be a much-advanced version that looks like this ax + by + c = 0. Here you can see two variables x and y. The highest degree of the given equations is 1. NCERT (https://ncert.nic.in/) Textbook Class 9 Maths Exercise 4.1 Solutions are useful for CBSE and State board students. Solutions of questions are given in PDF and Video format.

If we represent the linear equation in two variables in the Cartesian plane, we get a straight line. Similarly, if we draw two lines in the same Cartesian plane, they may intersect, coincide or parallel. In class 9 Maths Exercise 4.1, we will study about the plotting of a single line in two variable. We can draw a line using only two Cartesian points but for better accuracy we always take three points. It also verify that the plotted equation is correct.

You must’ve studied in the description that example will get you the exposure to how the question should be solved. Using the examples given in Exercise 4.1, one can represent the equations on the Cartesian plane . Understanding the example is important, for which you need to read all paragraph ex. 4.1. Here, you would understand, what are the steps to perform for the equations like 2x = – 5y, and -2x + 3y = 6 to plot in 2D plane.

There are certain points that one should carefully keep in mind. These points are important and given in before class IX Math exercise 4.1. (i) The solutions of a linear equation will be unaffected when (a) the same number is added to (or subtracted from) both the sides of the equations.

(b) You multiply or divide both the sides of the equation by the same non-zero number. The purpose of these points is to make you aware of a few extra points that can make, break or simplify the entire equation. It helps you during the solving equations.

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NCERT Solutions Class 9 Maths Chapter 4 Exercise 4.4 Linear Equations in two Variables

NCERT solutions for class 9 maths Chapter 4 exercise 4.4 linear equations in two variables comprise questions based on the geometrical representation of equations of lines parallel to x-axes and y-axes. The chapter ends with a summary of all the important topics and concepts for a quick revision of the linear equations in two variables. The exercises in the NCERT solutions class 9 maths chapter 4 exercise 4.4 linear equations in two variables have two questions that sufficiently cover this topic in detail.

While studying with the class 9 maths NCERT Solutions chapter 4 exercise 4.4, students will also gain the basic problem-solving approach that is vital for solving complex algebra problems, including linear equations. To learn about graphing of lines of equations parallel to x-axes and y-axes, download the NCERT solutions class 9 maths chapter 4 exercise 4.4 given below.

☛ Download NCERT Solutions Class 9 Maths Chapter 4 Exercise 4.4

Exercise 4.4 Class 9 Chapter 4   Download PDF

More Exercises in Class 9 Maths Chapter 4

• NCERT Solutions Class 9 Maths Chapter 4 Ex 4.2
• NCERT Solutions Class 9 Maths Chapter 4 Ex 4.3
• NCERT Solutions Class 9 Maths Chapter 4 Ex 4.4

NCERT Solutions Class 9 Maths Chapter 4 Exercise 4.4 Tips

Students will acquire an in-depth understanding of linear equations parallel to x-axes and y-axes by using the NCERT solutions class 9 maths Chapter 4 exercise 4.4. With the practice of the overall content provided in the NCERT Solutions for Class 9 Maths Exercise 4.4, students can grasp these concepts to understand and apply them efficiently.

The students should carefully practice and solve all the questions given in the exercise for great results. The notes provided at the end of the chapter are significant to improve the understanding of concepts that every student needs to learn and should have knowledge of.

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Class 9 Maths NCERT Solutions Video Chapter 4 Exercise 4.4

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• NCERT Solutions for Class 9 Maths Chapter 4: Linear Equations in Two Variables - Exercise 4.2
• NCERT Solutions

NCERT Solutions for Class 9 Maths Chapter 4 (Ex 4.2)

The best way to learn the concepts given in CBSE Class 9 Maths Exercise 4.2 is to download the NCERT Book Solutions for Class 9 Maths Chapter 4 Exercise 4.2. As you will be able to download the step by step study materials from Vedantu, then you will find not only the NCERT Solutions Class 9 Maths Chapter 4 but for all the chapters and which will help you to study more effectively. It will increase your confidence to appear in the exam by all means. Students can also avail of Class 9 Science NCERT Solutions from our website.

Access NCERT Solutions for Maths Chapter 4 - Linear Equations in Two Variables

1. Which one of the Following Options is True, and Why? \[\text{y=3x+5}\] has  

(i) A unique solution, 

(ii) only two solutions, 

(iii) infinitely many solutions

Ans. We are given that \[y=3x+5\] is a linear equation. 

For \[x=0\] , \[y=5\] . Therefore, \[(0,5)\] is a solution of the equation. 

For \[x=1\] , \[y=8\] . Therefore \[(1,8)\] is another solution of the equation. 

For \[x=2\] , \[y=11\] . Therefore \[(2,11)\] is another solution of the equation. 

Clearly, for different values of \[x\] , we get another distinct value of \[y\] .  

So, there is no end to different solutions of a linear equation in two variables. Therefore, a linear equation in two variables has infinitely many solutions.

Hence (iii) is the correct answer.  

2. Write Four Solutions for Each of the Following Equations:

(i) \[\text{2x+y=7}\]

Ans. Given equation \[2x+y=7\] , can be written as,

Let us now take different values of \[x\] and substitute in the above equation-

For \[x=0\] ,

So, \[(0,7)\] is a solution.

For \[x=1\] ,

So, \[(1,5)\] is a solution.

For \[x=2\] ,

So, \[(2,3)\] is a solution.

For \[x=3\] ,

So, \[(3,1)\] is a solution.

Therefore, the four solutions of \[2x+y=7\] are \[(0,7)\] , \[(1,5)\] , \[(2,3)\] , \[(3,1)\] .

(ii) \[\pi \text{x+y=9}\]

Ans. Given equation \[\pi x+y=9\] , can be written as,

\[y=9-\pi x\]

So, \[(0,9)\] is a solution.

\[y=9-\pi \]

So, \[(1,9-\pi )\] is a solution.

\[y=9-2\pi \]

So, \[(2,9-2\pi )\] is a solution.

\[y=9-3\pi \]

So, \[(3,9-3\pi )\] is a solution.

Therefore, the four solutions of \[\pi x+y=9\] are \[(0,9)\] , \[(1,9-\pi )\] , \[(2,9-2\pi )\] , \[(3,9-3\pi )\] .

(iii) \[\text{x=4y}\]

Ans. Given equation \[x=4y\] .

Let us now take different values of \[y\] and substitute in the above equation-

For \[y=0\] ,

So, \[(0,0)\] is a solution.

For \[y=1\] ,

So, \[(4,1)\] is a solution.

For \[y=2\] ,

So, \[(8,2)\] is a solution.

For \[y=3\] ,

So, \[(12,3)\] is a solution.

Therefore, the four solutions of \[x=4y\] are \[(0,0)\] , \[(4,1)\] , \[(8,2)\] , \[(12,3)\].

3. Check Which of the Following are Solutions of the Equation \[x-2y=4\] and Which are not:

(i) \[(0,2)\]

Ans. Substituting \[x=0\] and \[y=2\] in the L.H.S. of the given equation \[x-2y=4\] :

\[\Rightarrow 0-2(2)\]

\[\Rightarrow -4\]

Since \[L.H.S.\ne R.H.S.\] , therefore \[(0,2)\] is not a solution of the equation.

(ii) \[(2,0)\]

Ans. Substituting \[x=2\] and \[y=0\] in the L.H.S. of the given equation \[x-2y=4\] :

\[\Rightarrow 2-2(0)\]

\[\Rightarrow 2\]

Since \[L.H.S.\ne R.H.S.\] , therefore \[(2,0)\] is not a solution of the equation.

(iii) \[(4,0)\]

Ans. Substituting \[x=4\] and \[y=0\] in the L.H.S. of the given equation \[x-2y=4\] :

\[\Rightarrow 4-2(0)\]

\[\Rightarrow 4\]

Since \[L.H.S.=R.H.S.\] , therefore \[(4,0)\] is a solution of the equation.

(iv) \[(\sqrt{2},4\sqrt{2})\]

Ans. Substituting \[x=\sqrt{2}\] and \[y=4\sqrt{2}\] in the L.H.S. of the given equation \[x-2y=4\] :

\[\Rightarrow \sqrt{2}-2(4\sqrt{2})\]

\[\Rightarrow -7\sqrt{2}\]

Since \[L.H.S.\ne R.H.S.\] , therefore \[(\sqrt{2},4\sqrt{2})\] is not a solution of the equation.

(v) \[(1,1)\]

Ans. Substituting \[x=1\] and \[y=1\] in the L.H.S. of the given equation \[x-2y=4\] :

\[\Rightarrow 1-2(1)\]

\[\Rightarrow -1\]

Since \[L.H.S.\ne R.H.S.\] , therefore \[(1,1)\] is not a solution of the equation.

4. Find the value of \[k\] , if \[x=2\] , \[y=1\] is a solution of the equation \[2x+3y=k\] .

Ans. We are given the equation \[2x+3y=k\] along with the values \[x=2\] and \[y=1\] .

Substituting the given values in the L.H.S. of the equation:

\[\Rightarrow 2(2)+3(1)=k\]

\[\Rightarrow 4+3=k\]

\[\Rightarrow k=7\]

Therefore, we get \[k=7\] on solving the equation.

Linear Equations in Two Variables Class 9 – Exercise 4.2 Questions

If you are a student of class 9 and going to prepare for your examination and your school comes under the Central Board of Secondary Education then you must look at these solutions for NCERT Questions Class 9 Maths. NCERT Solutions are very helpful and it will help you to score good marks in the examination. In this study material, you will find all the contents as per the syllabus. The syllabus of class 9 Maths consists of 9 chapters. You will get immense help from the class 9 maths NCERT solutions chapter 4 exercise 4.2 content. The NCERT maths class 9 chapter 4 exercise 4.2 is beneficial for you for sure.

The topics and subtopics in the first chapter which is Number System are Introduction to Number System, Irrational Numbers, Real Numbers and their Decimal Expansions, Representing Real Numbers on the Number Line, Operations on Real Numbers, Laws of Exponents for Real Numbers.

The second chapter is Polynomials where you will learn about topics and subtopics like Polynomials in One Variable, Zeros of a Polynomial, Remainder Theorem, Factorisation of Polynomials and Algebraic Identities.

Coordinate Geometry is the third chapter where you can learn some calculations like The relative position of an object present in a plane, distance between two bodies present in different planes, Location of points in the real dimension (X-Y-Z axis), Classification of a plane - division into axes, Calculating equations based on coordinate points.

The NCERT Solutions for Class 9 Maths Chapter 4 is Linear Equations in Two Variables. The topics and subtopics are Linear Equations, Solution of a Linear Equation, Graph of a Linear Equation in Two Variables, Equations of Lines Parallel to the x-axis and y-axis. You can download free PDFs of NCERT Solution for Class 9 Maths Chapter 4 Exercise 4.2. You will not only be able to download the PDF of NCERT Solutions of Maths Class 9 Chapter 4 Exercise 4.2 but you can also download all the PDFs of other chapters and Exercises. Class 9th Maths NCERT Solutions Chapter 4 Exercise 4.2 will help to solve some calculations like how to write Linear Equations in Two Variables, how to express any linear equation in any form. From the NCERT Maths Solution Class 9 Chapter 4 Exercise 4.2 you will learn other calculations like draw graphs of Linear Equations in Two Variables, draw a line after plotting some points on the graph and many others. The NCERT solutions for class 9 maths chapter 4 exercise 4.2 has been tailored to help you solve all these problems with aplomb.

 In the Exercise 4.2 Class 9 Maths, the first question is a multiple choice type. To answer the second question, students will have to write four solutions for each of the given questions. Maths NCERT Solutions Class 9 Chapter 4 Exercise 4.2 will help to clear all your doubts about the chapter because it's designed in that way. Chapter 4 maths class 9 exercise 4.2 will certainly help you get more marks.

The fifth chapter of the syllabus Is Introduction to Euclid's Geometry where you will be learning about Euclid's Definitions, Axioms and Postulates, Equivalent Versions of Euclid's Fifth Postulate. You can look at the given exercises to solve your problems.

The sixth chapter Lines and Angles deal with the basic geometrical application of angles and their relationships with lines where you will learn how angles are formed when two lines intersect each other and when one line intersects more than one parallel line at different points to form distinct angels.

The topics and subtopics of the seventh chapter Triangles are Congruence of Triangles, Criteria for Congruence of Triangles, Some Properties of a Triangle, Some More Criteria for Congruence of Triangles, Inequalities in a Triangle.

In the chapter eight, Quadrilaterals, you will know about how to find the angles of a given quadrilateral, prove a hypothesis and consider that the diagonal of a quadrilateral are equal and prove that it is a rectangle. You will learn that if the diagonals of a quadrilateral bisect at right angles then it can be established as a rhombus. You will also learn many shortcut techniques to solve the problems properly from NCERT Solutions.

Areas of Parallelograms and Triangles is the 9th chapter and the topics and subtopics are Figures on the Same Base and Between the Same Parallels, Parallelograms on the Same Base and Between the Same Parallels, Triangles on the Same Base and Between the Same Parallels.

The 10th chapter is Circle, and the topics and subtopics are Circles and its Related Terms; A Review, Angle Subtended by a Chord at a Point, Perpendicular from the Centre to a Chord, Circle through Three Points, Equal Chords and Their Distances from the Centre, Angle Subtended by an Arc of a Circle, Cyclic Quadrilaterals.

Basic Constructions and Some Constructions of Triangles in chapter Eleven are the two topics in the eleventh chapter Constructions. To make this chapter easier, you can solve the exercises given in the book.

The twelfth chapter Heron's Formula will give you an introduction of topics like Area of a Triangle - by Heron's Formula, Application of Heron's Formula in Finding Areas of Quadrilaterals. NCERT Solutions covers all the exercises of the chapters, you will get help from them also.

The topics and subtopics of the chapter 13 Triangles are Surface Area of a Cuboid and a Cube, Surface Area of a Right Circular Cylinder, Surface Area of a Right Circular Cone, Surface Area of a Sphere, Volume of a Cuboid, Volume of a Cylinder, Volume of a Right Circular Cone, Volume of a Sphere.

The chapter Statistics is the 14th chapter of the syllabus and the topics and subtopics are Collection of Data, Presentation of Data, Graphical Representation of Data, Measures of Central Tendency.

The fifteenth and the last chapter is Probability. You need a clear idea of what Probability is to solve the problems of this chapter. Probability is the possible number of outcomes divided by the total number of outcomes. Probability is a part of Statistics. You can practice all the exercises where you will get the latest shortcut techniques to understand better.

Some Tips to Study Before the Examination

It is obvious that if you don't start from the beginning of your academic year then you will get too much pressure from studies before the examination. Mathematics is the subject where the key to success is practice. Try to solve some problems every day and if you find Maths is very tough then you will have to spend extra time on this subject.

Always keep a small diary or notebook with you, where you can note every math formula of your syllabus and important notes. This will help you to study effectively and you can look at this notebook whenever you forget something important about the subject. This will also help you with your last-minute preparation before the exam. And make sure that you have all the study materials in front of you on the study table so that you will not have to spend time in search of them.

Try to get up early in the morning and start your day with the study routine that you have created. You can study mathematics and science in the first few hours of the day if you find these subjects a little more difficult than the others. Don't get distracted from playing games or watching TV, try to avoid these things during the preparation or make a proper time table to these things after a full day study. Eat healthy foods and drink plenty of water and don't forget to have proper sleep at night as this can give you headaches. Don't try to clear your doubts before a few days of the examination, those days are for revision. If you have any doubts about anything then clear them with the help of Vedantu.

NCERT Solutions Class 9 Maths - PDF Availability

On the website of Vedantu, you will get a download option for the latest PDFs of the NCERT Solutions which is prepared and reviewed by subject experts. You will find the best study material as per the syllabus from here which will help you with your exam preparation. There are links for step by step free PDF downloads. You will learn many short cut techniques which will help to study smart and you will surely get good marks in the examination. You can not only download the PDFs for NCERT Solution of Maths Class 9 Chapter 4 Exercise 4.2 but also for all subjects. With the help of the most preferred study materials, you will not only be able to secure good marks in the examination but you can also be the master of any subject. If you want to study only to pass the exam then you will not be able to go for further studies then you will have to study in detail about the subject which will be required in future. Class 9 maths exercise 4.2 solutions are the best bet for your needs when it comes to studying efficiently.

About Vedantu

Vedantu is the no.1 online tutoring platform in India from where students will be able to learn from the live classes with some of the experienced teachers, some of them are from IIT. Vedantu has more than 500 teachers who have already taught about more than 40000 students for 1 million hours. They have spread their business across 30+ countries and 1000+ cities. The word Vedantu is a Sanskrit word where Veda stands for Knowledge and Tantu stands for Network. The name Vedantu is absolutely correct according to what they are doing. Their aim is to break the rules of traditional teaching and make learning fun and effective.

Currently, they are teaching subjects like Physics, Chemistry, Biology, Mathematics, German, French, English, Sanskrit, Computer Science, Environment Science and many more. They also provide coaching for competitive exams like Joint Entrance Examination. They teach students from class 4th to 12th for Indian Certificate of Secondary Education and the Central Board of Secondary Education. They have experienced teachers who have experience more than 10 years in teaching. Vedantu uses whiteboarding tools and a two-way audio-video system where students can read and write by watching the live classes and students can also respond to the teachers. They have a group and individual classes available for the students. Vedantu offers the best study (NCERT) solutions for faster and more effective learning. 

FAQs on NCERT Solutions for Class 9 Maths Chapter 4: Linear Equations in Two Variables - Exercise 4.2

1. What are the Solutions of Linear equation in 2 variables on a graph?

The  Solutions of Linear equation in 2 variables on a graph will be : 

Any linear equation in the standard form ax+by+c=0 has a pair of solutions (x,y), that can be represented in the coordinate plane.

When an equation is represented graphically, it is a straight line that may or may not cut the coordinate axes.

A linear equation ax+by+c=0 is represented graphically as a straight line.

Every point on the line is a solution for the linear equation.

Every solution of the linear equation is a point on the line.

2. when do a pair of linear equations with two variables have no solution.

If the two linear equations have equal slope value, then the equations will have no solutions.

m 1  = m 2 . This is because the lines are parallel to each other and do not intersect.

3. What happens to Linear equation in 2 variables when (i) Lines passing through the origin (ii) Lines parallel to coordinate axes.

In a Linear equation in 2 variables

(i) Lines Passing Through the Origin

Certain linear equations exist such that their solution is (0,0). Such equations when represented graphically pass through the origin.

The coordinate axes x-axis and y-axis can be represented as y=0 and x=0 respectively.

(ii) Lines Parallel to Coordinate Axes

Linear equations of the form y=a, when represented graphically are lines parallel to the x-axis and a is the y-coordinate of the points in that line.

Linear equations of the form x=a, when represented graphically are lines parallel to the y-axis and a is the x-coordinate of the points in that line.

4. How to score well in Algebra?

Algebra is most students' scoring friend. Unlike arithmetic and geometry it does not have any theorems to prove or complicated word problems. Most of the problems in algebra can be solved through logic. Students can develop this logical thinking through repeated practise of algebra problems. Along with this students will have to know basic formulas of algebra and some popular algebraic expressions. All these combined together will help students to score effectively and efficiently high marks in maths. Along with these, students can also refer the follows study materials in order to be able to score well in algebra as well as overall in Maths: 

Previous Year Question Papers

Exemplar Solutions

NCERT Solutions 

Sample Papers

All the above study materials are provided by Vedantu as free PDF for the students to download. These study resources are curated keeping in mind the need for the students to understand maths rather than just mugging it up.

5. Is NCERT enough for Chapter 4 of Class 9 Maths?

You should strictly adhere to the NCERT book and complete all the exercises of Chapter 4 of Class 9 Maths. You should also review the NCERT questions and go through the solved examples in the chapter to ensure that there are no errors. To guarantee more precision and less room for error, use the NCERT Solutions for Chapter 4 Class 9 Maths available free of cost. If you still have time, you can go over some questions from the supplemental reference books.

6. How to make notes of Chapter 4 of Class 9 Maths?

Make notes in a clear, readable handwriting that contains all equations, definitions, theorems, solved examples, and NCERT exercises. It won't take long if you finish it while preparing for your test. Also, make certain that your notebook is in good functioning order so that you can refer to it if you have a doubt or need to study for the exam. Also refer to the NCERT Solutions and other study material available on Vedantu app and website, to be thorough with Chapter 4 of Class 9 Maths.

7. How to study for Class 9 Maths Chapter 4?

Before you start solving the questions in Chapter 4 of Class 9 Maths, read it thoroughly and compile a list of the statements, definitions, and theorems found within. This is important because we frequently focus just on the issues and ignore the theoretical aspects of mathematics. You will receive straight marks on the theoretical section of the test. If you understand the keywords and use them in your answers, you will earn full credit.

8. How to ensure full marks in Maths Class 9 Chapter 4?

Once you've finished your curriculum, you should practise the question papers of this chapter from prior sessions' examinations. This does not imply that you should start any question paper at the last minute. You should begin practising the previous year's questions if you have a solid understanding of Chapter 4. You must review your work when you have completed it to identify where you are missing. Seeing your mistakes motivates you to fix them and consider how you might avoid them in the main exam.

9. How to plan a study schedule for Chapter 4 of Class 9 Maths?

To plan a study schedule, you must first prepare a list of your priorities and what you find difficult. This can be done according to the weightage each chapter carries and then you must focus on the difficult chapter with more weightage of marks. Then prepare a relevant schedule that will meet your needs and change it as you progress through the syllabus. Which is to say that when you complete the syllabus, you can devote more time to revisions and so on. Before going on to the chapter assignments, you must first practise by working through the NCERT book's solved examples. You'll gradually master this approach and gain a deeper understanding of how concepts form and then score great marks in your examination.

NCERT Solutions for Class 9

Cbse study materials for class 9, cbse study materials.

CBSE NCERT Solutions

NCERT and CBSE Solutions for free

Class 9 Mathematics Assignments

We have provided below free printable Class 9 Mathematics Assignments for Download in PDF. The Assignments have been designed based on the latest NCERT Book for Class 9 Mathematics . These Assignments for Grade 9 Mathematics cover all important topics which can come in your standard 9 tests and examinations. Free printable Assignments for CBSE Class 9 Mathematics , school and class assignments, and practice test papers have been designed by our highly experienced class 9 faculty. You can free download CBSE NCERT printable Assignments for Mathematics Class 9 with solutions and answers. All Assignments and test sheets have been prepared by expert teachers as per the latest Syllabus in Mathematics Class 9. Students can click on the links below and download all Pdf Assignments for Mathematics class 9 for free. All latest Kendriya Vidyalaya Class 9 Mathematics Assignments with Answers and test papers are given below.

Mathematics Class 9 Assignments Pdf Download

We have provided below the biggest collection of free CBSE NCERT KVS Assignments for Class 9 Mathematics . Students and teachers can download and save all free Mathematics assignments in Pdf for grade 9th. Our expert faculty have covered Class 9 important questions and answers for Mathematics as per the latest syllabus for the current academic year. All test papers and question banks for Class 9 Mathematics and CBSE Assignments for Mathematics Class 9 will be really helpful for standard 9th students to prepare for the class tests and school examinations. Class 9th students can easily free download in Pdf all printable practice worksheets given below.

Topicwise Assignments for Class 9 Mathematics Download in Pdf

More assignments for class 9 mathematics.

Advantages of Class 9 Mathematics Assignments

• As we have the best and largest collection of Mathematics assignments for Grade 9, you will be able to easily get full list of solved important questions which can come in your examinations.
• Students will be able to go through all important and critical topics given in your CBSE Mathematics textbooks for Class 9 .
• All Mathematics assignments for Class 9 have been designed with answers. Students should solve them yourself and then compare with the solutions provided by us.
• Class 9 Students studying in per CBSE, NCERT and KVS schools will be able to free download all Mathematics chapter wise worksheets and assignments for free in Pdf
• Class 9 Mathematics question bank will help to improve subject understanding which will help to get better rank in exams

Frequently Asked Questions by Class 9 Mathematics students

At https://www.cbsencertsolutions.com, we have provided the biggest database of free assignments for Mathematics Class 9 which you can download in Pdf

We provide here Standard 9 Mathematics chapter-wise assignments which can be easily downloaded in Pdf format for free.

You can click on the links above and get assignments for Mathematics in Grade 9, all topic-wise question banks with solutions have been provided here. You can click on the links to download in Pdf.

We have provided here topic-wise Mathematics Grade 9 question banks, revision notes and questions for all difficult topics, and other study material.

We have provided the best collection of question bank and practice tests for Class 9 for all subjects. You can download them all and use them offline without the internet.

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• Chapter 4: Linear Equation In Two Variables
• Exercise 4.3

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

In section 4.4 of Chapter 4 of NCERT Maths textbook for Class 9, under the headline “Graph of a Linear Equation in Two Variables”, it is concluded that every point on the line satisfies the equation of the line and every solution of the equation is a point on the line. The chapter deals with the concept of Linear Equations more in-depth. The exercises from page number 74 of the textbook are explained in clear and easy-to-understand steps by our subject matter experts in the NCERT Solutions for Class 9 Maths Chapter 4 – Linear Equation in Two Variables Exercise 4.3. The solutions, based on the NCERT syllabus, are prepared as per the guidelines.

Each concept is explained properly and clearly, with easy-to-understand examples and maths problems. We have devised the most accurate NCERT solutions for all the questions under each exercise after thorough research. It helps students to prepare well for the board exams.

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

Access answers of maths ncert class 9 chapter 4 – linear equations in two variables exercise 4.3.

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Access other exercise solutions of Class 9 Maths Chapter 4 – Linear Equations in Two Variables

Exercise 4.1 Solutions

Exercise 4.2 Solutions

Exercise 4.4 Solutions

1. Draw the graph of each of the following linear equations in two variables:

(i) x+y = 4

To draw a graph of linear equations in two variables, let us find the points to plot.

To find the points, we have to find the values that x and y can have, satisfying the equation.

Substituting the values for x,

When x = 0,

When x = 4,

The points to be plotted are (0, 4) and (4,0).

(ii) x–y = 2

When x = 2,

The points to be plotted are (0, – 2) and (2, 0).

When x = 1,

The points to be plotted are (0, 0) and (1, 3).

(iv) 3 = 2x+y

To draw a graph of linear equations in two variables, let us find out the points to plot.

To find out the points, we have to find the values which x and y can have, satisfying the equation.

The points to be plotted are (0, 3) and (1, 1).

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

We know that an infinite number of lines pass through a point.

The equation of 2 lines passing through (2,14) should be in such a way that it satisfies the point.

Let the equation be 7x = y

When x = 2 and y = 14

(7×2)-14 = 0

L.H.S. = R.H.S.

Let another equation be 4x = y-6

(4×2–14+6 = 0

Since both the equations satisfy the point (2,14), then we can say that the equations of two lines passing through (2, 14) are 7x = y and 4x = y-6

We know that an infinite number of lines pass through one specific point. Since there is only one point (2,14), here, there can be infinite lines that pass through the point.

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

The given equation is

According to the question, x = 3 and y = 4

Now, substituting the values of x and y in the equation 3y = ax+7,

(3×4) = (a×3)+7

⟹ 12 = 3a+7

⟹ 3a = 12–7

The value of a, if the point (3,4) lies on the graph of the equation 3y = ax+7 is 5/3.

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

Total distance covered = x

Total fare = y

Fare for the first kilometre = 8 per km

Fare after the first 1km = 5 per km

If x is the total distance, then the distance after one km = (x-1)km

i.e., fare after the first km = 5(x-1)

According to the question,

The total fare = Fare of first km+ fare after the first km

y = 8+5(x-1)

y = 8+5x – 5

Solving the equation,

When y = 0,

The points to be plotted are (0, 3) and (-3/5, 0)

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

(ii) x+y = 0

(iii) y = 2x

(iv) 2+3y = 7x

The points given in figure 4.6 are (0,0), (-1,1), (1,-1).

Substituting the values for x and y from these points in the equations, we get,

(0,0) ⟹ 0 = 0

(-1, 1) ⟹ -1 ≠ 1 ————————— equation not satisfied

(1, -1) ⟹ 1≠ -1 ————————— equation not satisfied

(0,0) ⟹ 0+0 = 0

(-1, 1) ⟹ -1+1 = 0

(1, -1) ⟹ 1+(-1) =0

(0,0) ⟹ 0 = 2×0

(-1, 1) ⟹ 1 = 2×(-1)

1≠ -2 ————————— equation not satisfied

(1, -1) ⟹ -1 = 2×1

-1 ≠ 2 ————————— equation not satisfied

(0,0) ⟹ 2+(30) = 7×0

2 ≠ 0 ————————— equation not satisfied

(-1, 1) ⟹ 2+(3×1) = 7×-1

5 ≠ -7 ————————— equation not satisfied

(1, -1) ⟹ 2+(3×-1) = 7×1

-1 ≠ 7 ————————— equation not satisfied

Since only equation x+y = 0 satisfies all the points, the equation whose graphs are given in Fig. 4.6 is

For Fig. 4. 7

(i) y = x+2

(ii) y = x–2

(iii) y = –x+2

(iv) x+2y = 6

The points given in figure 4.7 are (0,2), (2,0), (-1,3)

(0,2) ⟹2 = 0+2

(2, 0) ⟹ 0= 2+2

0 ≠ 4 ————————— equation not satisfied

(-1, 3) ⟹ 3 = -1+2

3 ≠ 1 ————————— equation not satisfied

(0,2) ⟹ 2 = 0–2

2 ≠ -2 ————————— equation not satisfied

(2, 0) ⟹ 0 = 2–2

(-1, 3) ⟹ 3= –1–2

3 ≠ –3 ————————— equation not satisfied

(0,2) ⟹ 2 = -0+2

(2, 0) ⟹ 0 = -2+2

(-1, 3) ⟹ 3= -(-1)+2

(0,2) ⟹ 0+(2×2) = 6

4 ≠ 6 ————————— equation not satisfied

(2, 0) ⟹ 2+(2×0) = 6

2 ≠ 6 ————————— equation not satisfied

(-1, 3) ⟹ -1+(2×3) = 6

5 ≠ 6 ————————— equation not satisfied

Since only equation y = –x+2 satisfies all the points, the equation whose graphs are given in Fig. 4.7 is

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

Let the distance travelled by the body be x and the force applied on the body be y.

It is given that,

The work done by a body is directly proportional to the distance travelled by the body.

y = 5x (5 is a constant of proportionality)

(i) when x = 2 units,

then y = 5×2 = 10 units

(ii) when x = 0 units,

then y = 5×0 = 0 units

The points to be plotted are (2, 10) and (0, 0).

7. Yamini and Fatima, two students of Class IX of a school, together contributed ₹ 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 ₹ x and ₹ y.) Draw the graph of the same.

Let Yamini’s donation be ₹x and Fatima’s donation be ₹y

According to the question;

We know that,

when x  = 0 , y = 100

when x = 50, y = 50

when x = 100, y = 0

The points to be plotted are (0,100), (50,50), and (100,0).

8. In countries like USA and Canada, the 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:

(i) Draw the graph of the linear equation above using Celsius for the x-axis and Fahrenheit for the 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.

(i) According to the question,

F = (9/5)C + 32

When C = 0, F = 32

When C = -10 , F = 14

The points to be plotted are (0, 32), (-10, 14).

(ii) When C = 30,

F = (9/5)C +32

F = (9×30)/5+32

(iii) When F = 95,

95 = (9/5)C +32

(9/5)C = 95-32

C = (63×5)/9

(iv) When C = 0,

F = (9×0)/5 +32

When F = 0,

0 = (9/5)C+32

(9/5)C = 0-32

(9/5)C = -32

C = (-32×5)/9

(v) When F = C,

C = (9/5)C+32

C – (9/5)C = 32

(5-9)C/5 =32

(-4/5)C = 32

(-4/5)C = (-32×5)/4

Hence, -40 o is the temperature which is numerically the same in both Fahrenheit and Celsius.

In this exercise, there are 8 questions, where question 1 has the main question with 3 sub-questions under it, where students could be asked to draw a graph of the given linear equations. Additionally, question numbers 2 and 3 are short answer questions, whereas question numbers 4, 5, 6 and 7 are long answer questions. Finally, question number 8 from the exercise has 1 main question and 8 sub-questions under it.

We have provided detailed and chapter-wise solutions for the questions under each exercise. Students can access the detailed exercise solutions of NCERT Solutions For Class 9 Maths from the PDF link given above. It will help them to get practice solving different types of questions: The Solutions also help to

• Get an overall idea about the topic
• Clear doubts about the Linear Equation Concepts
• Learn the formula related to equations relevant to this concept
• Gain practice from solving questions

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• CBSE- Linear Equations in two variables

Linear Equations in two variables-Test

Test    HOTS Questions    Notes    MCQ    NCERT Solutions    Sample Questions   

• STUDY MATERIAL FOR CBSE CLASS 9 MATH
• Chapter 1 - Area of Parallelograms and Triangles
• Chapter 2 - Circles
• Chapter 3 - Constructions
• Chapter 4 - Coordinate Geometry
• Chapter 5 - Herons Formula
• Chapter 6 - Introduction to Euclids Geometry
• Chapter 7 - Linear Equations in two variables
• Chapter 8 - Lines and Angles
• Chapter 9 - Number Systems
• Chapter 10 - Polynomials
• Chapter 11 - Probability
• Chapter 12 - Quadrilaterals
• Chapter 13 - Statistics
• Chapter 14 - Surface Areas and Volumes
• Chapter 15 - Triangles

Chapter 4 – Algebraic Expressions and Algebraic Formulas

Exercise 4.1, exercise 4.2, exercise 4.3, exercise 4.4, review exercise, multiple choice questions, this post has 19 comments.

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In review ex q 5 (3)³ is 27 but you have wrote 9

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In review ex q 5 you hav wrote (3)³ but you have to write 3²

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I need math exercise 4.4 exercise class 9

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