NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables (Ex 3.4) Exercise 3.4

Class 10 is a defining phase in a student’s academic career. It gets students ready for the harder courses they will encounter in higher education. Additionally, admissions to schools offering higher secondary education are occasionally based on grade point averages from Class 10. To make good future choices, Class 10 students must perform well on the board examination conducted by the CBSE. In Class 10, students are required to study a variety of difficult subjects. Studying these subjects sometimes puts students under pressure. The pressure they feel as a result of their preparation can have an adverse effect on how well they perform on the board exam. Hence, they need to have a solid preparation strategy in place so that they can give their best in the board exams. They should also have adequate study materials and preparation resources. Extramarks provides a number of study tools that can be utilised to read through and revise each subject.

Mathematics is one of the most crucial subjects for students in Class 10. Getting good grades in Mathematics requires a lot of studying. Each chapter must be thoroughly understood. Students also need to practise answering numerous questions in order to properly comprehend the concepts. But sometimes it is difficult for Class 10 students to study so many subjects. Students feel overwhelmed by the various rules and formulae in the textbook. The NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4 and other exercises made available on the Extramarks platform are hence recommended for students to use as they practise NCERT exercises. One of the most challenging subjects for students to grasp is Mathematics. Class 10 is a crucial year since it lays the foundation for their future professional lives. The majority of students struggle with the incredibly intimidating mix of Mathematics and Class 10. However, if it is practised and taught properly, Mathematics may develop into a genuinely exciting subject. Students from all boards of education across the nation struggle with this subject. The CBSE’s Mathematics curriculum for Class 10 covers topics that are logic and concept-focused, in contrast to other subjects. When students are able to understand the concepts, they can perform well on their tests. That is when the Extramarks platform steps in to assist CBSE Class 10 students. To aid in their understanding of the ideas more quickly and thoroughly, students can use interactive study tools from Extramarks that include 3D video modules made by subject-matter experts. Students need a variety of tools to help them prepare for their exams, including the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4. With the help of the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4, students may comprehend the various types of questions that appear on the question paper and get ready for the board exams. The NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4 will teach students effective strategies for responding to the question paper. In order to perform well in exams, it is essential for students to practise with NCERT solutions, such as the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4.

Class 10 Maths Chapter 3 Exercise 3.4 of the NCERT book is about A Pair of Linear Equations in Two Variables. The topics that students learned in their previous classes are continued in a number of ways in this chapter. This chapter applies a variety of concepts that students have learned in previous classes. In this chapter, new concepts are also introduced to students. This chapter goes into great detail about these topics. To understand the idea behind these topics, students should study them in depth. They will not be able to master these ideasby reading alone, , though. For this reason, the NCERT book contains a good number of examples and exercises. To fully understand the topics, students need to work through all the examples and exercises. Students run into a number of difficulties while attempting to solve these problems, which prevents them from effectively finishing the exercises.The examples in this chapter of the NCERT book have detailed step-by-step solutions; however, the exercises do not. The NCERT book only offers conclusive answers to the exercises’ questions, without going into further depth. Students must comprehend the procedures involved in obtaining the answers to the questions while working through these problems. Students must therefore have access to the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4.

NCERT Solutions Class 10 Maths Chapter 3 Exercise 3.4

Even when NCERT Solutions are accessible online, regular offline access is preferred. By having offline access, students can study whenever and wherever they want without connecting to the internet. Extramarks offers students access to the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4 for usage whenever they want to learn. Unexpected network issues and poor internet connectivity will therefore no longer be a barrier to learning. The expert-curated NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4 provide a chance for study and exam practise by covering all the problems in the exercises. Students can download the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4 in PDF format for continuous test preparation from the Extramarks website and mobile app.

Access NCERT Solutions for Class 10 Maths Chapter 3 – Pair of Linear Equations in Two Variables

If students have access to the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4, they would be more able to comprehend the ideas presented in the NCERT textbook. They will also be well-versed in the answers and approaches to each type of question. None of the questions in the NCERT exercises has a detailed explanation. On the Extramarks website, students can acquire the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4. For students to better comprehend the course conceptually, the Extramarks website and mobile app provide NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4.

NCERT Solutions for Class 10 Maths Chapter 3 Exercise 3.4 

Accessing the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4 on the internet can be difficult. Moreover, it can be difficult to confirm the authenticity of the solutions even when students have access to the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4. Extramarks offers the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4 so that students do not have to go elsewhere. On the Extramarks website and mobile app, they can find the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4. They can easily find the PDF version for the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4 and finish the exercises whenever it is most convenient for them. Extramarks offers thorough answers to each question given in the exercises in the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4 to help students evaluate their performance.

Difference Between Substitution Method and Elimination method

The chapter on Pair of Linear Equations in Two Variables is a vital chapter for a student to study. Students will benefit from the concepts covered in this chapter not only in the board exams, but also in other areas.The chapter teaches students to solve a pair of linear equations that contain two variables. Students can learn various methods of solving such equations as the Graphical Method, Substitution Method, Cross-Multiplication Method and Elimination Method. In the substitution method, students can solve the equations by expressing the value of one variable in terms of another. In the elimination method, equations are solved by one variable first to get a linear equation of one variable and solve this equation. Students should practise all these methods to be able to solve any type of question that is posed to them. Moreover, they should also practice numerous questions from the exercises to find the method that is most convenient for them. This way can solve such questions faster.

NCERT Solutions for Class 10 Maths Chapter 3 Exercises

The chapter on Pair of Linear Equations in Two Variables includes six exercises in total, with an optional exercise at the end. Students can learn various methods of solving equations by completing each of these exercises. Exercise 3.1 covers questions on basic understanding of linear equations in two variables. It contains three questions in total. Exercise 3.2 includes seven questions that are based on the Graphical method of solving the equations. Exercise 3.3 includes three questions that are based on the Substitution method. Exercise 3.4 Class 10 Maths includes two questions that are based on the Elimination method. Students can refer to the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4 to help in solving these questions. Exercise 3.5 includes four questions that are based on the Cross-multiplication method. Exercise 3.6 includes two questions that cover the topic of Equations Reducible to a Pair of Linear Equations in Two Variables. Furthermore, Exercise 3.7 includes questions covering the entire chapter. There are eight questions in this exercise. Students should solve all the exercises to be thorough with this chapter and score higher marks.

Benefits of NCERT Solutions for Class 10 Maths

The NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4 on Extramarks can help students in a number of ways.Students can get help with difficult problems by using the detailed, step-by-step solutions provided in the NCERT Solutions for Class 10 Maths Chapter 3 Exercise 3.4.. In order to tackle difficult mathematical problems, they must be segmented. The answer to this issue can be found in the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4. Their grasp of the most tricky topic improves when they use the NCERT textbook. By comparing their answers to the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4, students can assess themselves and their progress. The extensively examined and fact-checked NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4 are accessible on Extramarks. Even if there are many websites that provide these answers, their accuracy remains in doubt. Students must use reliable study materials due to the importance of the board exams. The authenticity of the solutions that Extramarks provides has been confirmed by teachers. Clear language is used to explain the comprehensive NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4 and other chapters. Students are advised on the most effective method for organising their answers. They offer the most effective and simple solutions to mathematical problems.

Finding the finest online resource to help students in Class 10 achieve their academic objectives might be difficult despite the abundance of tools available. NCERT solutions offer the right and necessary response to their educational expectations. Students who are studying for their board examinations can find the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4. Another advantage is that the CBSE itself encourages using the NCERT textbook. The NCERT textbooks are used in the CBSE curriculum. Exam-relevant practise questions can be found in abundance in the NCERT textbooks. These questions frequently leave students perplexed, which lowers their confidence in the topic and the material. The first topic is where understanding the concepts begins. When tackling the questions in the NCERT textbooks, students who have access to the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4 will benefitfrom having a solid understanding of both fundamental and complicated concepts. Students who successfully complete this will have a solid conceptual understanding of the subject. By contrasting their responses with the solutions, they can also evaluate themselves and make corrections.

The NCERT exercises are the most crucial resource for preparing questions for the board exams.Hence, students are often advised to answer the NCERT textbook exercise questions. In order to evaluate their answers, they also require the right answers to the questions. Thus, the NCERT solutions enable students to receive the assistance they require while getting ready for the board exams. By using the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4, students can apply the concepts from the chapter in a better and more precise manner. The thorough and error-free NCERT Solutions for Class 10 Maths, Chapter 3 Exercise 3.4 were written by teachers with advanced trainingWhen developing these solutions, the mental capabilities of Class 10 students were taken into account. The complex problems have been divided into smaller, more manageable parts to make writing answers to the questions given in this exercise easier. Teachers frequently emphasise the importance of detailed, stepwise answers. Students should closely follow the instructions in the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4 for maximum scores. Since many of the formulas provided in the NCERT textbook are difficult for students to understand and remember, they are unable to use them to answer the exercises’ problems. However, if students practise using the step-by-step solutions in the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4, it will be easier for them to remember the formulas and utilise them correctly.

Understanding the multiple concepts covered in the Class 10 Mathematics syllabus requires receiving the appropriate guidance. It can be difficult to succeed in subjects like Mathematics, and the stress of the tests only makes it harder. Students can get the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4 from the top subject specialists in addition to using other sorts of assistance to fully comprehend the concepts in a particular topic. Students can get the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4 from prominent subject specialists along with the carefully created study resources provided by Extramarks.Not only that, but with the assistance of subject specialists, students will feel confident in their study plan and for upcoming tests.To help students get ready for the board exam and other competitive exams like Olympiads, Class 10 includes a number of assessments at the school level. However, in order to do well on many tests, students require expert guidance. For test preparation, having access to the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4 could be very useful.

Along with the NCERT Solutions for Class 10 Maths Chapter 3 Exercise 3.4, ExtraMath also has NCERT solutions for other chaptersStudents may get comprehensive and in-depth NCERT solutions on Extramarks for each of the 15 chapters in the NCERT textbook for Mathematics. Additionally, complete answers to the questions from the various exercises have been provided. Teachers frequently assign NCERT exercises to students as part of their homework. The questions present a number of challenges for students to overcome. They occasionally are unable to finish the assignments. If students have access to the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4, they can still do their homework easily. After doing their schoolwork on time, students can go on to do their scheduled activities. They will then be able to finish their coursework on time and prepare effectively in accordance with their plan. Since these answers are given in simple language, students can readily comprehend them and effectively apply the techniques to solve the problems. NCERT solutions are offered on Extramarks for a variety of subjects in addition to Mathematics. Students can use the NCERT solutions on Extramarks to complete their homework assignments for all subjects.

NCERT Solutions Class 10  Mathematics are available on Extramarks for all 15 chapters of the NCERT textbook, in addition to  NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4. In addition, Class 12 students studying for their board exams can locate the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4 for Mathematics and other disciplines. NCERT Solutions are available for all the subjects taken by students in other classes as well. On Extramarks, one may access NCERT Solutions Class 8, NCERT Solutions Class 11, NCERT Solutions Class 9, NCERT Solutions Class 7, NCERT Solutions Class 12, and NCERT Solutions Class 6. Furthermore, Extramarks offers NCERT solutions for primary classes, including NCERT Solutions Class 2, NCERT Solutions Class 5, NCERT Solutions Class 3, NCERT Solutions Class 4 and NCERT Solutions Class 1. On the Extramarks website and mobile app, students may obtain the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4 in a downloadable PDF format. The NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4 can be very helpful for students in their test preparation, as the NCERT textbook is recommended by the CBSE.NCERT Solutions for Class 10 Maths

Q.1

Solve the following pair of linear equations by theelimination method and the substitution method:(i)   x + y = 5 and 2x – 3y = 4(ii)  3x + 4y = 10 and 2x – 2y = 2(iii) 3x – 5y – 4 = 0 and 9x = 2y + 7(iv) x2 + 2y3 = –1 and x –y3 = 3

Ans.

(i) By elimination method:Given that        x+y=5 ...(1) 2x−3y=4 ...(2)We multiply equation (1) by 3 and then add it toequation (2) to eliminate the variable y and getthe value of x as follows.                  3x+3y=15                  2x−3y=4 ¯                   5x          =19or                  x=195Using this value of x in equation (1), we get                      195+y=5or y=5−195=65By substitution method:From equation (1), we get                   y=5−xSubstituting this in equation (2), we get                  2x−3  (5−x)=4or 5x=4+15=19or x=195Substituting this value of x in equation (1), we get                    195+y=5or y=5−195=65

(ii) By elimination method:Given that      3x+4y=10 ...(1) 2x−2y=2          ...(2)We multiply equation (2) by 2 and then add it toequation (1) to eliminate the variable y and getthe value of x as follows.                  3x+4y=10                  4x−4y=4 ¯                   7x          =14or               x=2Using this value of x in equation (1), we get                      6+4y=10or y=10−64=1By substitution method:From equation (2), we get                   x=1+ySubstituting this in equation (1), we get                  3 (1+y)+4y=10or    7y=10−3=7or y=1Substituting this value of y in equation (2), we get                    2x−2=2or x=2+22=2

(iii) By elimination method:Given that      3x−5y−4=0             ...(1) 9x=2y+7                           ...(2)We multiply equation (1) by 3 and then subtract equation (2) from it to eliminate the variable x and getthe value of y as follows.                 9x−15y−12=0                  9x                      =2y+7−                             −     − ¯                          −15y−12=−2y−7or               −15y+2y=−7+12=5or y=−513Using this value of y in equation (2), we get                      9x=−513×2+7or x=−10117+79=−10+91117=81117=913By substitution method:From equation (2), we get                   x=2y+79Substituting this in equation (1), we get                  3  ×2y+79−5y−4=0or    2y+73−5y=4or 2y+7−15y=12or −13y=12−7or y=−513Substituting this value of y in equation (2), we get                    9x=−2×513+7=−10+9113or x=8113×9=913

(iv) By elimination method:Given that      x2+2y3=−1             ...(1) x−y3=3                           ...(2)We multiply equation (2) by 2 and then add it toequation (1) to eliminate the variable y and getthe value of x as follows.                 x2+2y3=−1                   2x−2y3=6¯                  x2+2x=5or               5x2=5or x=2Using this value of x in equation (2), we get                      2−y3=3or −y=3  (3−2)=3or y=−3By substitution method:From equation (2), we get                   x=3+y3Substituting this in equation (1), we get                  12  (3+y3)+2y3=−1or   9+y6+2y3=−1or 9+y+4y6=−1 or 9+y+4y=−6or y=−155=−3Substituting this value of y in equation (2), we get                     x=3+−33=2

Q.2 Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:
(i) If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes ½ if we only add 1 to the denominator. What is the fraction?

(ii) Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?

(iii) The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

(iv) Meena went to a bank to withdraw ₹ 2000. She asked the cashier to give her ₹50 and ₹100 notes only. Meena got 25 notes in all. Find how many notes of ₹ 50 and ₹100 she received.

(v) A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid ₹ 27 for a book kept for seven days, while Susy paid ₹ 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.

Ans.

(i)Let the fraction be xy.According to question,      x+1y−1=1    ⇒x+1=y−1⇒x−y=−2 ...(1)Also,        xy+1=12⇒ x=y+12⇒ 2x=y+1⇒ 2x−y=1           ...(2)Subtracting equation (2) from equation (1), we get             x=3Substituting this value in equation (1), we gety=5Hence, the fraction is 35.

(ii)Let the present age of Nuri and Sonu be x yearsand y years respectively.So, five years ago,Nuri‘s age=(x–5) yearsandSonu’s age=(y–5) yearsAccording to question,       x−5=3  (y–5)⇒  x−5=3y−15⇒  x−3y=−10                ...(1)Again, Ten years hence,Nuri‘s age=(x+10) yearsandSonu’s age=(y+10) yearsAccording to the question,   x+10=2(y+10)or x−2y=10             ... (2)Subtracting equation (2) from equation (1), we gety=20Putting this value in (2), we getx=50Hence, Nuri and Sonu are 50 yearsand 20 years old respectively.

(iii)Let the two digit number be 10x+y.According to question,            x+y=9               ...(1)and        9 (10x+y)=2 (10y+x)⇒ 90x+9y=20y+2x⇒ 90x−2x+9y−20y=0⇒ 88x−11y=0⇒ 8x−y=0 ...(2)Adding equations (1) and (2), we getx = 1Putting this value of x in equation (2), we gety=8Hence, Number=10x+y=10+8=18

(iv)Let number of notes of ₹50 and ₹100bexandyrespectively.According to question,            x+y=25               ...(1)and       50x+100y=2000⇒ 50 (x+2y)=2000⇒ x+2y=40 ...(2)Subtracting equation (1) from equation(2), we getx+2y=40x+y=25−   −         −  ¯        y=15Putting this value in equation (1), we getx=10Hence, Meena received 10 notes of ‘50 and 15 notes of ‘100.

(v)Let the fixed charge for first three day be ₹x and additionalcharge for each day thereafter be ₹y.According to question,            x+4y=27               ...(1)and       x+2y=21      ...(2)Subtracting equation (2) from equation (1), we getx+4y  =27x+2y=21−   −         −  ¯        2y=6or y=3Putting this value in equation (1), we getx=27−12=15Hence, fixed charge is ₹15 and additional charge foreach extra day is ₹3.

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FAQs (Frequently Asked Questions)

1. Where can Class 10 students find the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4?

On the Extramarks website and mobile app, students can find the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4. Students can access and download the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4 online in PDF format. They can get offline access to the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4 so that they can use them whenever and wherever they want without needing to use the internet.

2. How should students use the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4 when studying for exams?

First, students should read the chapter from the start to the end. All the formulas and methods of solving the equations should be learnt. The NCERT textbook examples should be studied next. By doing so, students will discover several methods for resolving the chapter’s questions. After completing the examples, they should attempt the exercises’ questions. They must try to answer the questions without looking at the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4. As soon as they are finished, students can look at the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4 to check their answers. They must correct their errors and learn the methods outlined in the solutions if they are to successfully answer the questions. After that, they should retry answering the exercises’ questions to see how much they have improved. They will perform better on exams since they will be more equipped to comprehend the chapter’s contents and solve various types of equations.

3. What topics and concepts are included in the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4?

The chapter on Pair of Linear Equations in Two Variables is covered in the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4. It contains different methods of solving the equations including the Graphical Method, Substitution Method, Cross-Multiplication Method and Elimination Method. To fully understand the chapter, students should pay close attention to each topic and work through the exercises’ questions.

If students use the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4 during the board exam, will they be able to complete the question paper in the allotted time?

Students should practice the NCERT textbook questions every day if they wish to complete the exam paper in the allowed time. Students’ writing becomes quicker as a result of often practising the questions. Questions from the NCERT textbooks are also included on the exam paper. In order to finish the exam question paper quickly, students can use the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4 and understand the different methods of solving equations.

4. What advantages do students gain from using the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4?

In the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.4 provided by Extramarks, all of the exercises’ questions are addressed. It includes both basic and complex application-based questions. Each question in Exercise 3.4 Maths Class 10 has been solved completely. All the problems have been solved by following all the necessary steps to arrive at the answer. Students can use these solutions with assurance to get precise answers to all the questions in the exercise. These problems have correct solutions that are explained in a comprehensible manner. Students can score higher on their exams if they correctly respond to these questions. If they have already practised these questions, they will find it easier to respond to all of them when they take their board exams.

The Extramarks website or mobile application can be accessed by students for more information and access to multiple learning resources and much more.