Mathematics is an important subject for all competitive examinations. The subject cannot be mugged up and hence, needs a detailed approach to every problem. Students must study this subject by understanding the concepts well. NCERT Solutions Class 9 Mathematics Chapter 4 provides accurate answers to the NCERT questions of the chapter which gives you in-depth knowledge about the subject and concepts to be studied.
The Linear chapter equations in two variables cover the following topics; solutions to linear equations, graphs of linear equations in two variables, and equations of the line passing through the X and Y axis. It is directly connected with the Linear chapter equations in one variable covered in NCERT Class 8 Mathematics. Hence, students are advised to revise the concepts given in the NCERT Class 8 textbook before reading this chapter and brush up on their concepts.
You can find quick revision points along with the core concepts required from previous classes in our NCERT Solutions for Class 9 Mathematics Chapter 4. This would help you give a clear-cut idea of what terminologies you have to keep in mind while reading this chapter. Apart from this, it also includes highlight points of all the topics and sub-topics from NCERT Class 9 Mathematics textbook, which will help in building the strong concept of the chapter.
Extramarks’ website is a complete source of information for the students studying in Class 1st to Class 12th. It has NCERT study materials, NCERT revision notes, NCERT textbooks, NCERT Exemplar and Past years’ papers, making it the most useful platform online for the teachers and students.
Key Topics Covered In NCERT Solutions Class 9 Mathematics Chapter 4
Students can understand Linear equations in two variables in a proper way only if they have a proper understanding of Linear equations in one variable already covered in NCERT Class 8 Mathematics textbook. Hence, students are advised to revisit the important points given in NCERT Class 8 Mathematics to quickly recall the concepts. The chapter strongly requires students to use their Mathematical solving skills. It also requires one to be comfortable with solving the equations.
We cover everything required to be noted in this chapter in NCERT Solutions for Class 9 Mathematics Chapter 4, available on the Extramarks website. Extramarks website is the right source to rely upon for your preparation as it includes all the learning material required to score well and upgrade your performance in your academics.
We have included the following key topics in our NCERT Solutions for Class 9 Mathematics Chapter 4:
| Exercise |
Topic |
| 4.1 |
Introduction |
| 4.2 |
Linear Equations |
| 4.3 |
Solution of a Linear Equation |
| 4.4 |
Graph of a Linear Equation in two variables |
| 4.5 |
Equations of lines parallel to X-axis and Y-axis |
Once you complete Chapter 4 Mathematics Class 9, you will be capable of solving some of the important topics of NCERT Class 11 and NCERT Class 12 Mathematics. As a result, you will start developing an interest in Algebra and look for in-depth knowledge of the topics.
4.1 Introduction
The chapter begins with the general introduction of Linear equations in one variable covered in NCERT Class 8 Mathematics. Further, it states its interrelation with Linear equations in two variables. The chapter is included in NCERT Class 9 Mathematics.
You will find the definition of linear equations in one and two variables, along with examples in our NCERT Solutions for Class 9 Mathematics Chapter 4.
4.2 Linear Equations
An equation is a combination of a constant and variables under equality. When the equation includes its variables in their simplest form, like x,y,z etc., it is called a linear equation.
For example, 7x+5=6 is a linear equation.
When a linear equation has two variables instead of one, it is called linear equations in two variables.
For example, 3y-2z=9 is a linear equation in two variables
Steps to note while solving an equation:
- If a number is added to or subtracted from LHS, the same number will be added to or subtracted from RHS
- Similarly, if a number is multiplied to or divided from LHS, the same number will be multiplied to or divided from RHS
- You can solve the linear equations in two variables only and only if you have two given equations
4.3 Solution of a Linear Equation
You have already studied that a linear equation in one variable has a unique solution. Does this hold true for linear equations in two variables too? Let us explore this in this section.
As we know, a linear equation in two variables has two variables. There are high chances of finding more than one solution.
For example: Consider the equation 2x+3y = 12.
The solution for this equation is x=3 and y=2 as it satisfies RHS. It is written in the ordered pair as (3,2). Similarly, the other solutions for this equation are (0,4) and (6,0).
Hence, it is concluded that a linear equation in two variables may or may not have a unique solution.
You can practice more such examples from our NCERT Solutions for Class 9 Mathematics Chapter 4.
4.4 Graph of linear equations in two variables
In the last section, you have already learnt how to find different sets of solutions for linear equations in two variables. In this section, we will learn how to plot the obtained solutions on a graph.
Just like Coordinate Geometry, you have to draw a Cartesian system on the graph, and then by locating the different values of solutions obtained, you have to plot points by drawing proper lines.
4.5 Equations of lines parallel to X-axis and Y-axis
When a linear equation in two variables is written in the form y=0, it is called an equation of a line parallel to the X-axis. Likewise, when a linear equation in two variables is written in the form x=0, it is called an equation of a line parallel to the Y-axis.
Get the complete chapter study material along with NCERT Solutions for Class 9 Mathematics Chapter 4 on the Extramarks website today and see your child clear every examination with flying colours.
NCERT Solutions for Class 9 Mathematics Chapter 4 Exercise & Solutions
Extramarks website has NCERT Solutions for Class 9 Mathematics Chapter 4, which includes a detailed analysis of the Chapter along with revision notes. This will help you to level up your performance in different stages of preparation and go beyond what is expected as a Class 9th student.
You can find for exercise specific questions and solutions for NCERT Solutions for Class 9 Mathematics Chapter 4 by referring to the following links:
- Chapter 4: Exercise 4.1 Question and answers
- Chapter 4: Exercise 4.2 Question and answers
- Chapter 4: Exercise 4.3 Question and answers
- Chapter 4: Exercise 4.4 Question and answers
Along with NCERT Solutions for Class 9 Mathematics Chapter 4, students can explore NCERT Solutions on our Extramarks website for all primary and secondary classes.
- NCERT Solutions Class 1
- NCERT Solutions Class 2
- NCERT Solutions Class 3
- NCERT Solutions Class 4
- NCERT Solutions Class 5
- NCERT Solutions Class 6
- NCERT Solutions Class 7
- NCERT Solutions Class 8
- NCERT Solutions Class 9
- NCERT solutions Class 10
- NCERT solutions Class 11
- NCERT solutions Class 12
NCERT Exemplar for Class 9 Mathematics
NCERT Exemplar Class 9 Mathematics book is the collection of various questions required to be good performers in the subject of Mathematics. The different types and ranges of questions covered throughout the book will prove to be a milestone in every aspect of your Mathematics studies.
These books will help to develop an interest in the subject at large. You will also learn to get insights and learn to use various concepts of Mathematics in your day to day life. The benefits provided in this book will make an overall difference in your score in competitive examinations. It covers all the Chapters in-depth, which makes it fruitful for all the students.
After referring to the NCERT Solutions and NCERT Exemplar, the students develop more practical oriented thinking, which is the key aspect of anything you study as it helps in better understanding of the concepts. As a result, students can jump to more advanced and higher-level conceptual questions. By studying from the Exemplar, you can constantly assure yourself to be the next topper.
Key Features of NCERT Solutions for Class 9 Mathematics Chapter 4
You can gain momentum in your preparation only and only if all your doubts are cleared. Hence, NCERT Solutions for Class 9 Mathematics Chapter 4 offers a complete solution for all problems. The key features are provided:
- You can find quick referral links to all the exercises questions in NCERT Solutions for Class 9 Mathematics Chapter 4.
- You can solve numerical type as well as Integer type questions with the help of Extramarks NCERT Solutions.
- After completing the NCERT Solutions for Class 9 Mathematics Chapter 4, you will enhance your problem solving skills and will be able to retain formulas and concepts involved in it for a long time.