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NCERT Solutions for Class 9 Maths Chapter 4 - Linear Equations in Two Variables Exercise 4.1

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NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables Exercise 4.1 - FREE PDF Download

NCERT Class 9 Maths Chapter 4 Exercise 4.1 Solutions - Linear Equations in Two Variables, introduces students to the fundamental concepts of linear equations. This exercise focuses on understanding how to represent and solve linear equations in two variables, which is a crucial part of algebra. Students will learn to identify and plot solutions on a graph, enhancing their analytical and graphical skills.


Vedantu’s Class 9 Maths NCERT Solutions provide clear, step-by-step explanations, making it easier for students to grasp these concepts. Mastering these basics is essential for solving more complex problems in future chapters and exams.


Glance on NCERT Solutions Maths Chapter 4 Exercise 4.1 Class 9 | Vedantu

  • Linear equations are algebraic expressions where each term is either a constant or the product of a constant and a single variable.

  • Linear equation in two variables, the highest power of the variables is one.

  • The general form of a linear equation in two variables is ax+by+c=0.

  • Linear equations can be graphically represented as straight lines on a coordinate plane.

  • Solutions to linear equations in two variables are ordered pairs that make the equation true.

  • These equations are fundamental for understanding relationships between quantities and for solving real-life problems.

  • Understanding how to solve and graph linear equations builds a strong foundation for more advanced algebraic concepts.

  • There are two questions in Maths Ex 4.1 Class 9 which are fully solved by experts at Vedantu.

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Access NCERT Solutions for Maths Class 9 Chapter 4 - Linear Equations in Two Variables Exercise 4.1

1. 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 Rs. \[\text{x}\] and that of a pen to be Rs. \[\text{y}\] ) 

Ans. Let the cost of a notebook be Rs. \[x\] and the cost of a pen be Rs. \[y\] .

We know that the cost of a notebook is twice the cost of a pen.

Therefore, we can write the required linear equation in the form:

\[Cost\text{ }of\text{ }notebook\text{ }=\text{ }2\text{ }\times \text{ }Cost\text{ }of\text{ }pen~~\]

\[x=2y~\]

\[x-2y~=0\] 

2. Express the following linear equations in the form \[\text{ax+by+c= 0}\] and indicate the values of \[\text{a}\] , \[\text{b}\] , \[\text{c}\] in each case: 

(i) \[\text{2x+3y=9}\text{.3}\overline{\text{5}}\]

Ans. Writing the given equation in standard form \[\text{ax+by+c= 0}\] :

\[2x+3y=9.3\overline{5}\]

\[2x+3y-9.3\overline{5}=0\]

Comparing this equation with standard form of the linear equation, \[\text{ax+by+c= 0}\] we have:

\[a=2\]

\[b=3\]

\[c=-9.3\overline{5}\]

(ii) \[\text{x-}\frac{\text{y}}{\text{5}}\text{-10=0}\]

Ans. Writing the given equation in standard form \[\text{ax+by+c= 0}\] :

\[x-\frac{y}{5}-10=0\]

\[5x-y-50=0\]

Comparing this equation with standard form of the linear equation, \[\text{ax+by+c= 0}\] we have:

\[a=5\]

\[b=-1\]

\[c=-50\]

(iii) \[\text{-2x+3y=6}\] 

Ans. Writing the given equation in standard form \[\text{ax+by+c= 0}\] :

\[-2x+3y=6\]

\[-2x+3y-6=0\]

Comparing this equation with standard form of the linear equation, \[\text{ax+by+c= 0}\] we have:

\[a=-2\]

\[b=3\]

\[c=-6\]

(iv) \[\text{x=3y}\]

Ans. Writing the given equation in standard form \[\text{ax+by+c= 0}\] :

\[x=3y\]

\[x-3y=0\]

Comparing this equation with standard form of the linear equation, \[\text{ax+by+c= 0}\] we have:

\[a=1\]

\[b=-3\]

\[c=0\]

(v) \[2x=-5y\] 

Ans. Writing the given equation in standard form \[\text{ax+by+c= 0}\] :

\[2x=-5y\]

\[2x+5y=0\]

Comparing this equation with standard form of the linear equation, \[\text{ax+by+c= 0}\] we have:

\[a=2\]

\[b=5\]

\[c=0\]

(vi) \[\text{3x+2=0}\]

Ans. Writing the given equation in standard form \[\text{ax+by+c= 0}\] :

\[3x+2=0\]

Comparing this equation with standard form of the linear equation, \[\text{ax+by+c= 0}\] we have:

\[a=3\]

\[b=0\]

\[c=2\]

(vii) \[\text{y-2=0}\] 

Ans. Writing the given equation in standard form \[\text{ax+by+c= 0}\] :

\[y-2=0\]

Comparing this equation with standard form of the linear equation, \[\text{ax+by+c= 0}\] we have:

\[a=0\]

\[b=1\]

\[c=-2\]

(viii) \[\text{5=2x}\]

Ans. Writing the given equation in standard form \[\text{ax+by+c= 0}\] :

\[5=2x\]

\[-2x+5=0\]

Comparing this equation with standard form of the linear equation, \[\text{ax+by+c= 0}\] we have:

\[a=-2\]

\[b=0\]

\[c=5\]


Conclusion

NCERT Solutions for Class 9 Maths Chapter 4 - Linear Equations in Two Variables, Exercise 4.1, helps students master the basics of linear equations. Understanding the relationship between variables and practising these problems is crucial for building a strong foundation. Practising Exercise 4.1 improves speed, accuracy, and conceptual clarity, helping students excel in their exams. Solving this exercise with Vedantu's detailed solutions provides clear explanations, making learning easier and more effective.


Class 9 Maths Chapter 4: Exercises Breakdown

Exercise

Number of Questions

Exercise 4.2

4 Questions with Solutions


CBSE Class 9 Maths Chapter 4 Other Study Materials


Chapter-Specific NCERT Solutions for Class 9 Maths

Given below are the chapter-wise NCERT Solutions for Class 9 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.


FAQs on NCERT Solutions for Class 9 Maths Chapter 4 - Linear Equations in Two Variables Exercise 4.1

1. Why are Class 9 students recommended to download NCERT Solutions for Maths Chapter 4 Linear Equations in Two Variables Exercise 4.1?

Students are advised to download NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables Exercise 4.1 as it is the best study material available to learn the chapter properly. It helps students to find answers to all the exercise questions in one place. Students will be able to solve problems where equations with two variables are involved with the help of NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables Exercise 4.1. In case of having any doubts in the exercise, students can refer to these solutions without any second thoughts. The study material is provided by subject matter experts at ed-tech platforms like Vedantu at no cost. The solutions are provided in a step-by-step manner to ensure students can learn them on their own. Vedantu provides well-prepared NCERT Solutions designed as per the latest guidelines and syllabus to help students score well in exams.

2. How to procure NCERT for class 9 maths chapter 4 exercise 4.1 solutions?

Students can procure exercise-wise NCERT Solutions for ex 4.1 class 9 in a free to download PDF format on Vedantu’s site. Vedantu is a known name in the e-learning sector. Students who are facing difficulty in solving ex 4.1 class 9 CBSE Maths can avail the solutions on Vedantu’s site provided by expert tutors. This is an important chapter, as questions on Linear Equations in Two Variables will help students solve higher-level problems of Maths. Hence, students must solve all the problems and refer to Vedantu’s site for solutions.

3. Why is Vedantu a popular choice for exercise-wise NCERT class 9 maths chapter 4 exercise 4.1 solutions?

Exercise-wise NCERT Solutions for Class 9 Maths Chapter 4 and other chapters by Vedantu are the most comprehensive and well-researched study material. NCERT Solutions for class 9th maths chapter 4 exercise 4.1, as well as other exercises, are prepared according to how it is explained in the example questions given in the textbook. NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables is a popular choice among students as it helps them to improve their understanding of the chapter and provide effective revision. 

4. What are the types of questions in class 9 maths 4.1?

There are two types of questions asked in class 9 maths ch 4 ex 4.1. The first question is a problem statement which has to be represented as a linear equation in two variables. In the second question, there are certain equations given which have to be expressed in the form of ax + by + c = 0. The exercise will help students to understand how to express linear equations in two variables correctly.

5. What is the best Solution book for NCERT for Class 9?

The best NCERT Solutions for Class 9 are provided by Vedantu. These solutions are prepared with complete precision and accuracy by subject experts who have several years of experience and are highly qualified. Before getting published, these solutions are checked several times and revised, if need be. Students who want to refer to the NCERT Solutions for Class 9 Maths can use NCERT Solutions for Class 9 from Vedantu.

6. Where can I get the NCERT Solutions for Maths Exercise 4.1 of Class 9?

When it comes to preparing for your exams, the NCERT Solutions are the most important study material that students must go through. They can download and refer to these Solutions while preparing for their exams. Vedantu’s NCERT Solutions for Chapter 4 Exercise 4.1 of Class 9 Maths are available for online as well as offline use for free. Students can find the answers to all questions from Chapter 4 in the Solutions. The solutions are available on the Vedantu Mobile app.

7. What should I focus on while solving class 9 maths Ch 4 Ex 4.1?

While solving class 9 maths 4.1, focus on understanding how to represent relationships between variables using linear equations. Practice solving these equations accurately to build a strong foundation. Ensure you understand the basics of formulating equations from word problems and interpret the relationships correctly. Regular practice will enhance your problem-solving skills and accuracy.

8. How can I have Class 9 NCERT Maths Solutions for reference?

The Vedantu Class 9 NCERT Maths Solutions are available in PDF format. To download the solutions, follow these steps:

  1. Click on this link

    1. On this page, you will find all the exercises.

    2. Click on the link for the exercise PDF you want. 

  2. The solutions PDF will be available on your screen. Click on the 'Download PDF' option to save the solutions for offline use.