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NCERT Textbook Solutions for Class 9 Mathematics Chapter 4, Linear Equations in Two Variables, provide a comprehensive understanding of concepts such as graphical representation and problem-solving techniques. NCERT 9th Math Exercise 4.1 focuses on introducing the basics of linear equations, while NCERT Textbook Maths Exercise 4.2 dives into plotting graphs to visually interpret solutions. Students often rely on PDF versions of these CBSE Book solutions for quick and accessible learning. Popular platforms like Tiwari Academy provide detailed solutions to all exercises, helping students strengthen their grasp of topics.
NCERT Exercises Solutions for Class 9 Maths Chapter 4: CBSE Board
Class 9 Mathematics chapter 4 is integral to understanding the graphical representation of equations, with practice questions emphasizing real-world applications. Whether students prefer notes, step-by-step explanations, or examples in Hindi, the NCERT detailed solutions cater to diverse needs. Resources simplify concepts, enabling students to solve challenging problems and prepare thoroughly for exams.
Class 9 Maths Exercise 4.1 in English
Class 9 Maths Exercise 4.2 in English
NCERT Book Class 9th Maths Chapter 4, Linear Equations in Two Variables, is a critical topic in building a strong foundation in algebra. With detailed solutions available for NCERT Math Exercises 4.3 and 4.4, students can master advanced problem-solving techniques. Resources from platforms such as Tiwari Academy offer curated NCERT Mathematics Textbook solutions tailored to CBSE Class 9 standards. Students frequently search for NCERT Solutions for Class 9 Maths Chapter 4 PDF download to access offline material for uninterrupted study.
Class 9 Maths Chapter 4 Solutions Guide: State Boards
The graphical approach to linear equations forms the core of this chapter, requiring practice with examples and key questions to excel. Notes provided by popular platforms highlight important steps, ensuring students understand the logic behind every solution. With engaging explanations and solved examples, these resources enable students to tackle Class 9 Maths NCERT Book Chapter 4 Exercises with confidence.
Class 9 Maths Chapter 4 Exercise 4.1
Class 9 Maths Chapter 4 Exercise 4.2
Class 9 Maths Chapter 4 Exercise 4.3
Class 9 Maths Chapter 4 Exercise 4.4
NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables in Hindi and English Medium for academic year 2024-25. We aimed to make the study of Class 9 Maths easier through its educational resources and solutions. Here are some ways in which Tiwari Academy may help make Class 9 Maths study easier for students. Solutions are updated as per new NCERT books for CBSE Session 2024-25 final exams.
Class 9 Maths Chapter 4 Solutions: Hindi Medium
Online platforms like Tiwari Academy have features that allow students to ask questions or seek clarification on specific problems or concepts. This can be valuable for addressing doubts and improving understanding. We offer additional resources such as video lectures, quizzes and study tips, which can enhance the overall learning experience.
Class 9 Maths Exercise 4.1 in Hindi
Class 9 Maths Exercise 4.2 in Hindi
NCERT Solutions for Class 9 Maths Chapter 4
NCERT Book Solutions for Class 9 Math Chapter 4 emphasize the importance of structured learning through practice. Examples of linear equations in two variables are presented with practical applications, encouraging students to relate theory to real-world scenarios. NCERT 9th Mathematics Solutions offered by platforms like Tiwari Academy include easy-to-understand methods for solving exercises and revising concepts efficiently. Graphical representation of equations, introduced early in NCERT Textbook Exercise 4.1, is further developed in subsequent exercises, preparing students for advanced algebra topics.
For Hindi-medium learners, NCERT Detail solutions in Hindi provide clear explanations to eliminate language barriers. Notes, practice questions and downloadable PDFs ensure that every student has access to quality educational resources. As the chapter lays a solid groundwork for higher classes, resources from platforms help students overcome challenges and excel in their Class 9 NCERT Book Maths exams.
| Class: 9 | Mathematics |
| Chapter 4: | Linear Equations in Two Variables |
| Number of Exercises: | 2 (Two) |
| Content: | NCERT Exercises Solutions |
| Content Type: | Images, Text and Video Format |
| Academic Session: | CBSE 2024-25 |
| Medium: | English and Hindi Medium |
Important Points in Class 9 Maths Chapter 4 for Board Exams
Definition: Linear equations in two variables and their standard form.
Graphical Representation: Plotting equations and identifying solutions.
Solutions: Understanding consistent, inconsistent and dependent equations.
Applications: Real-life problem-solving using linear equations.
Exam Focus: Practice Exercises 4.2, 4.3 and application-based questions.
| Day | Topic | Task | Resources |
|---|---|---|---|
| Day 1 | Introduction to Linear Equations | Read the theory and solve examples | NCERT textbook, notes |
| Day 2 | Exercise 4.1 | Solve all problems and verify answers | NCERT Solutions, reference books |
| Day 3 | Graphical Representation | Practice plotting graphs | Graph paper, online graphing tools |
| Day 4 | Exercise 4.2 | Solve graph-related problems | NCERT Solutions, teacher guidance |
| Day 5 | Applications of Linear Equations | Understand real-life examples | NCERT examples, case studies |
| Day 6 | Exercise 4.3 | Solve advanced problems | NCERT Solutions, practice papers |
| Day 7 | Revision | Review notes and solve mock questions | Sample papers, mock tests |
NCERT Solutions for Class 9 Maths Chapter 4
UP Board Solutions for Class 9 Maths Chapter 4 Prashnavali 4.1 and Prashnavali 4.2 are given below in Hindi Medium. View UP Board Solution and NCERT (https://ncert.nic.in/) Solutions for 2024-25 in Video Format Hindi Medium and English Medium or free download in PDF or use it as online all the digital contents. There is not any login or registration condition. Just visit to website and use the contents free of cost. For any inconvenience, contact us for help. We are here to help you without any charge. You can coordinate with us message via social media or text message. Visit to Tiwari Academy Online and Offline Apps page and download Class 9 Maths App for Offline use or Download Kaksha 9 Ganit App for offline use.
9th Maths Chapter 4 Solutions in English & Hindi Medium
NCERT Solutions for Class 9 Maths Chapter 4 all exercises are given below. NCERT Solutions 2024-25 are updated for the CBSE Exams 2021 based on Latest CBSE Syllabus 2024-25. NCERT Solutions and UP Board Solutions for Class 9 Maths Chapter 4 as online contents are helpful for all the CBSE, MP Board, Gujrat Board & UP Board (High School) students who are following NCERT Books for their Examination.
Important Notes on 9th Maths Chapter 4
An algebraic equation is a statement of equality of algebraic expression involving one or more variables. An equation which can be put in the form ax + by + c = 0, where a, b and c are real numbers (a and b together cannot be zero) and x, y are variables, is called a liner equation in two variables. A linear equation in one variable (say x) can be written as linear equation in two variables, by taking coefficient of other variable (say y) as zero.
Class 9 Maths Chapter 4 Practice Questions with Solutions
When is the solution of a linear equation is not affected?
The solution of a linear equation is not affected when
1.The same number is added to (or subtracted from) both sides of the equation.
2. Both sides of the equation are multiplied (or divided) by the same non-zero number.
What is meant by a solution of the linear equation?
The graph of every linear equation in two variables is a straight line and every point on the graph (straight line) represents a solution of the linear equation.
Class 9 Maths Chapter 4 Exercise 4.1 Solution in Hindi Medium
Important Point in 9th Maths Chapter 4
Important Questions on 9th Maths Chapter 4
Give the equations of two lines passing through (2, 14). How many more such lines are there, and why?
Equation of two lines passing through (2,14) are given by: x+y=16 and 8x-y = 2. There are infinite number of lines that can pass through (2, 4) as infinite number of lines passes through a point.
If the point (3, 4) lies on the graph of the equation 3y = ax + 7, find the value of a.
Given equation of line: 3y = ax + 7. Putting x = 3 and y = 4, we have, 3 × 4 = a × 3 + 7 ⇒ 12 = 3a + 7 ⇒ 12 – 7 = 3a ⇒ a = 5/3
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.
Given that: Distance traveled = x km and total fare = ₹ y Total fare = Fare for first km + Fare for remaining distance Therefore, the equation: y = 8 + 5×(x – 1) ⇒ y = 5x + 3
The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement. (Take the cost of a notebook to be ₹ x and that of a pen to be ₹ y).
Here, the cost of notebook = ₹ x and the cost of pen =₹ y According to question, Cost of notebook = 2 × Cost of Pen ⇒ x = 2y ⇒ x – 2y = 0
Express the following linear equation in the form ax + by + c = 0 and indicate the values of a, b and c: 2x + 3y = 9.35.
2x + 3y = 9.35 ⇒ 2x + 3y – 9.35 = 0 Hence, Here a = 2, b = 3 and c = – 9.35.
1. Every solution of the linear equation cab be represented by a unique point on the graph of the equation.
x = 0 is the equation of the Y- axis and y = 0 is the equation of the X-axis.
2. The graph of x = a represents a straight line parallel to the Y-axis and the graph of y = a represent a straight line parallel to the X-axis.
3. An equation of the type y = mx represents a straight line through the origin.
What is the importance of NCERT Solutions for Class 9 Maths Chapter 4?
NCERT Textbook Solutions for Chapter 4, Linear Equations in Two Variables, are essential for understanding the basics of algebra and graphical representation of equations. These solutions provide step-by-step methods to solve problems, making it easier for students to grasp complex concepts. The chapter is foundational for advanced topics in mathematics and helps develop logical reasoning and analytical skills. With detailed explanations, examples and exercises, the solutions cater to different learning styles, whether students prefer English or Hindi. They also ensure students are well-prepared for exams by including practice questions and real-world applications.
What are the main objectives of chapter 4 class 9th Maths?
The main objectives of chapter 4 Linear Equations in Two Variables of class 9th Maths are to teach students:
- The meaning of Linear Equations in Two Variables.
- How to find solutions of Linear Equations in Two Variables.
- How to draw the graph of Linear Equations in Two Variables.
- About equations of lines parallel to the x-axis and y-axis.
How can students effectively use NCERT Solutions for Chapter 4?
To make the best use of these solutions, students should first attempt solving exercises on their own and then refer to the solutions to verify their methods. Begin with simpler problems in NCERT Maths Exercise 4.1 and progressively move to more complex exercises like NCERT Textbook Exercises 4.3 and 4.4. Using notes and practice questions, students can strengthen their understanding of graphical methods and algebraic techniques. Regular practice with these solutions ensures mastery of linear equations and builds confidence. Downloading PDFs for offline access helps students revise anytime, ensuring thorough preparation for exams.
What are the main points of chapter 4 of class 9th Maths to remember for exam?
The main points of chapter 4 of class 9th Maths that students must remember at the time of exam are:
- An equation of the form ax + by + c = 0, where a, b and c are real numbers, such that a and b are not both zero, is called a linear equation in two variables.
- A linear equation in two variables has infinitely many solutions.
- The graph of every linear equation in two variables is a straight line.
- x = 0 is the equation of the y-axis and y = 0 is the equation of the x-axis.
- The graph of x = a is a straight line parallel to the y-axis.
- The graph of y = a is a straight line parallel to the x-axis.
- An equation of the type y = mx represents a line passing through the origin.
- Every point on the graph of a linear equation in two variables is a solution of the linear equation. Moreover, every solution of the linear equation is a point on the graph of the linear equation.
- An easy way of getting a solution is to take x = 0 and get the corresponding value of y. Similarly, we can put y = 0 and obtain the corresponding value of x.
What topics are covered in Chapter 4 of Class 9 Maths?
NCERT Textbook 9th Maths Chapter 4, Linear Equations in Two Variables, introduces students to the concept of equations with two variables and their graphical representation. It covers topics like forming equations, plotting graphs and finding solutions through different methods. Exercises are designed to build skills gradually, starting from basics in NCERT Book Exercise 4.1 to advanced problem-solving in NCERT 9th Mathematics Exercise 4.4. The chapter also emphasizes the practical application of linear equations in real-life situations. With practice, students learn to interpret and analyze graphs, providing a solid foundation for future topics in algebra and coordinate geometry.
Which exercise of chapter 4 of class 9th Maths has the highest number of sums?
In chapter 4 of class 9th Maths, there are four exercises.
The first exercise (Ex 4.1) contains two questions and two examples (examples 1, 2).
The second exercise (Ex 4.2) contains four questions and two examples (examples 3, 4).
So, the second exercise (Ex 4.2) has the highest number of sums.
Why is the graphical representation of linear equations important?
Graphical representation of linear equations is crucial because it provides a visual way to understand the relationship between variables. By plotting equations on a graph, students can identify the point of intersection, which represents the solution. This approach helps in better comprehension of abstract algebraic concepts. It also prepares students for topics like coordinate geometry and calculus, where visual interpretation plays a significant role. Exercises in 9th NCERT Maths Chapter 4 gradually introduce this concept, enabling students to relate mathematics to real-world problems, such as predicting trends and analyzing data patterns.
How can students get good marks in chapter 4, Linear Equations in Two Variables of 9th Maths?
Chapter 4 of class 9th Maths contains good examples and easy questions. All questions and examples of this exercise are nice and interesting. So, to get good marks in chapter 4 of class 9th Maths, students should practice all questions and examples of this chapter.
