NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5

Mathematics is one of the most important fields of study. It is concerned with logical reasoning and quantitative calculations. Mathematics plays a substantial role in everyday life. The knowledge of this subject can prove to be very useful in the everyday life of students. Students must pay close attention to the concepts that are taught in Class 10 Maths Chapter 3 Exercise 3.5. Mathematics is applied in almost all fields of life. Students particularly looking to make a career in Engineering must work on the development of their mathematical skills right from their schooling years to get a jump start. Students must pay attention to the mathematical concepts introduced in Class 10 since most of the competitive examinations are based on these mathematical concepts. Most of these competitive exams require logical reasoning abilities and quantitative aptitude. The concepts required to develop logical reasoning abilities and quantitative aptitude are mostly covered in the Mathematics Class 10 syllabus. Students planning to appear for competitive examinations like JEE Mains, JEE Advance, CAT, and NEET, should pay special attention to the mathematical concepts that are covered in Class 10. Students may utilise the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5 

Students are advised to take note of the fact that the Central Board of Secondary Education is responsible for conducting annual examinations for Class 10 and Class 12. Not just for the conduct of examinations, but CBSE is also responsible for the prescription and authorisation of conditions of examinations. The CBSE board examination is sourced from the NCERT curriculum. It is highly recommended that students use the NCERT books to study for the CBSE board examination. Students can also access the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5 from the Extramarks website to study for the CBSE Board Examination of Mathematics. The marks that students secure in the CBSE board examination play a huge part in availing opportunities to students in the field of their choice. Students may use the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5 for their preparation. It is advisable to refer to the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5 since the CBSE board examination is highly based on the NCERT curriculum. 

Students are advised to cover the NCERT syllabus thoroughly. It is important that they properly understand the concepts taught in the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5. Class 10 covers a wide range of topics, all of which require regular revision and practice. Solving NCERT exercise problems can be quite challenging sometimes. Students can take help from the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5 which can be found on the Extramarks website. Class 10 Mathematics syllabus can be quite difficult to comprehend. Students must take the preparation for the CBSE Board Examination of Class 10 Mathematics with utmost attention and sincerity. The NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5 can be referred to by students for their preparation.

NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5 – Pair of Linear Equations in Two Variables

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Pair of Linear Equations in Two variables is one of the most interesting as well as tough topics that have been covered in the syllabus of Chapter 3 Exercise 3.5 Class 10 Maths. Students have the provision of downloading the study material in PDF format from the Extramarks website. This feature has been introduced by Extramarks to facilitate learning resources for students who may not have constant access to an internet connection or whose internet connection might be poor. The NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5 can be downloaded in PDF format from the Extramarks website by students. Referring to downloaded documents can make it much easier and more convenient for students. 

The study material provided by Extramarks has a wide range. Extramarks provides online live sessions for students to have an enhanced learning experience. Students can also find access to past years’ papers for all CBSE examinations on the Extramarks website. Oftentimes, for many reasons like information overload, students may find it difficult to retain the information that they have studied for a longer period. To avoid this from happening, Extramarks provides revision notes that students can refer to for better retention of the study material. Students can access the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5 for better explained and elaborated solutions from the Extramarks website. Past years’ papers for all subjects of all examinations are also accessible on the Extramarks website. Students also have the provision of taking mock tests on the Extramarks website.

Taking mock tests can help students keep track of their progress in terms of their preparation for the CBSE board examination. Students can also obtain sample papers and solved examples from the Extramarks website and learning application. PDF files of sample papers and solved examples can also be downloaded from Extramarks. Practising can help students improve their speed of attempting the paper. Examining sample papers and solved examples can also give students insight into the topics that they are confident about and the topics that they need to go through in more depth. It is emphasised that students thoroughly practice the NCERT exercise problems with the help of the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5, considering the importance of the NCERT curriculum in the CBSE board examination. 

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

The NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5 are elaborated adequately for students to be able to understand better. Extramarks has systematically broken down the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5 into steps. The framework applied to the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5 is easy for students to understand and grasp. The study material provided by Extramarks can help students get a better hold of the concepts that are introduced and taught in the NCERT syllabus. Students must contribute more time to the chapters that have more weightage in the CBSE Board Examination of Mathematics Class 10. To secure high marks in the CBSE board examination, students should be aware of the latest examination pattern. Knowing the CBSE board examination pattern can help students in weeding out the dispensable information and focusing on learning and preparing from the adequate study material. 

Students can refer to Extramarks for information regarding the question paper pattern, examination structure, marks distribution, chapter weightage and marking scheme for the CBSE board examination. Senior secondary classes are one of the most crucial classes in the academic life of a student. Students must understand the gravity of the importance of the CBSE Board Examination of Class 10 Mathematics. A student’s performance in the CBSE board examination and their choice of the stream for Class 11 and Class 12 will also be responsible for dictating their further academic specialisation. Students must prepare for the CBSE Board Examination of Class 10 responsibly and with sincerity. Securing high marks in the senior secondary examinations can help open up avenues for students in a variety of fields. Students can make use of NCERT Solutions for their preparation for the CBSE Board Examination of Class 10. 

In Class 10, students take their first CBSE board examination. Students may find it challenging to move through the preparation process if they have limited knowledge and no experience with the Board examination. To assist students in their preparation, Extramarks offers several learning resources on the Extramarks website for students of all classes. The study material for Class 1 to Class 12 is available on the Extramarks website. The Extramarks website offers students access to the NCERT Solutions Class 1. The students can review the NCERT Solutions Class 2 on the Extramarks website. The NCERT Solutions Class 3 for all topics are available to students in PDF format on the Extramarks website and mobile application. For answers to all exercise problems, Class 4 students are advised to refer to the NCERT Solutions Class 4 on Extramarks. The Extramarks website and mobile application both offer the NCERT Solutions Class 5 in PDF format for students to download. Students can find the NCERT Solutions Class 6 of all chapters of all subjects in an organised manner on the Extramarks website. The NCERT Solutions Class 7 can be availed by students for better preparation from Extramarks.

For improved performance in exams, students of Class 8 can refer to the NCERT Solutions Class 8. The NCERT Solutions Class 9 is accessible to students of Class 9 for a better understanding of the concepts taught in the NCERT syllabus of Class 9. To prepare for the CBSE board examination, students can practice the NCERT Solutions Class 10. For the preparation for the CBSE Board Examination of Mathematics Class 10, students can also refer to the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5. Students of Class 11 can utilise NCERT Solutions Class 11 to get a hold of the concepts of the concerned syllabus. To gain a deeper knowledge of the concepts presented in the relevant syllabus, it is advised that students of Class 12 carefully read through all the NCERT Solutions Class 12 of all topics. It is highly recommended to refer to the NCERT syllabus as the CBSE board exam question paper pattern is based on the NCERT syllabus.

The NCERT curriculum syllabus is used as the primary document for the examination structure of the CBSE board examination. Students may access the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5 to study for the CBSE Board Examination of Mathematics chapter 3 of Class 10. The study material provided by Extramarks is curated by professionals from the point of view of competitive examinations. Students must understand all the concepts covered in the syllabus thoroughly as they can be a valuable addition to students’ knowledge from a long-term perspective. The knowledge that students acquire in their senior secondary academic years can help them in the future when they are appearing for competitive examinations. Extramarks provides learning resources that are detailed and comprehensive. Students are advised to refer to the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5 for a comprehensive understanding of the Mathematics syllabus of Class 10. 

Class 10 Chapter 3 Exercise 3.5 Solution: A Brief Overview

When the degree of an equation is one, it is called a linear equation. A linear equation is an equation in which the power of all the variables involved is one. Mathematics chapter 3 of Class 10, Pair of Linear Equations in Two Variables covers the technique of how to determine the value of a particular variable through various methods. Pair of Linear Equations in Two Variables is one of the most significant parts of the Class 10 Mathematics NCERT curriculum. This chapter holds a lot of weightage in the CBSE board examination. Pair of a Linear Equation in Two Variables is a chapter that covers a lot of mathematical concepts that are beneficial even in the future for students. Students must pay attention to the details of exercise 3.5 Maths Class 10 chapter 3 Pair of Linear Equations in Two Variables. It is essential to understand the basics of each topic to prepare the chapter effectively. Students must study the topics that are covered in the syllabus following their weightage in the CBSE board examination. This can help students prioritise the important topics and help them avoid wasting time and effort on topics that do not hold value in the CBSE board examination. 

Students may find Class 10 to be academically demanding, however, it is equally vital as it is demanding. Learning resources are available on Extramarks to aid students with exam preparation. It is one of the most well-known and trusted learning websites. Parents and students alike rely on it for quality study material. By signing up on the Extramarks website, they can access the study material and resources provided by Extramarks for a better and enhanced learning experience. Students must study with the help of the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5. The NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5 have been prepared following the CBSE board examination. Students are advised to practice the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5. Solving exercise problems and practising the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5 can help students to have a better grasp of the concerned topics.

What is a Cross Multiplication Method To Solve Linear Equations in One Variable? 

Students must thoroughly understand the cross multiplication method to solve linear equations in one variable, as it is one of the most important topics that have been covered in the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5. Students must diligently go through the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5 to thoroughly understand the mathematical concepts covered in the Mathematics chapter 3 of Class 10. Students should practice the NCERT exercise problems and solutions. Students may refer to the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5 from the Extramarks website or mobile application to study for the Class 10 CBSE Board. 

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NCERT Solutions for Class 10 Maths Chapter 3 Exercises

Students must perform well in the CBSE Board examination since it lays the groundwork for a bright future. While preparing for the CBSE Board Examination of Mathematics, students are advised to practice the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5. Students of Class 10 CBSE must focus on frequently practising Mathematics topics. Students must practice solving the NCERT exercise questions occasionally. Regularly solving the exercise problems can help students prepare well for the CBSE Board Examination. Students may refer to the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5 to solve the NCERT exercise problems. 

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Students may refer to the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5 available on Extramarks. Students can acquire study materials from the Extramarks website and mobile application to improve their exam preparations. The study material on Extramarks is regularly reviewed for errors and updated following the syllabus. Throughout the examination preparation process, students can continue referring to the study materials to increase their confidence. Class 10 students may utilise the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5 for the preparation for the CBSE Board Examination of Mathematics. The NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5 revision notes can also be acquired from the Extramarks website. 

 

Q.1

Which of the following pairs of linear equations has unique solution,no solution, or infinitely many solutions. In case there is a uniquesolution, find it by using cross multiplication method.(i) x – 3y –3 = 0                         (ii) 2x + y = 5    3x – 9y – 2 = 0                           3x + 2y = 8(iii) 3x – 5y = 20                         (iv)  x – 3y – 7 = 0          6x – 10y = 40                             3x – 3y – 15 = 0

Ans.

(i) x−3y−3=0      3x−9y−2=0Here, a1a2=13, b1b2=−3−9=13, c1c2=−3−2=32and soa1a2=b1b2≠c1c2Thus, the given pair of linear equations have no solution.(ii) 2x+y=5      i.e.,      2x+y−5=0        3x+2y=8      i.e.,      3x+2y−8=0Here, a1a2=23, b1b2=12, c1c2=58and soa1a2≠b1b2Thus, the given pair of linear equations have unique solution.By cross-multiplication method, we have        xb1c2−b2c1=yc1a2−a1c2=1a1b2−b1a2⇒    x−8−(−10)=y−15−(−16)=14−3⇒    x2=y1=11⇒    x=2 and y=1 (iii) 3x−5y=20         i.e.,      3x−5y−20=0         6x−10y=40        i.e.,       6x−10y−40=0Here, a1a2=36=12, b1b2=−5−10=12, c1c2=−20−40=12and soa1a2=b1b2=c1c2Thus, the given pair of linear equations have infinitelymany solutions.(iv) x−3y−7=0                  3x−3y−15=0 Here, a1a2=13, b1b2=−3−3=1, c1c2=−7−15=715and soa1a2≠b1b2Thus, the given pair of linear equations have unique solution.By cross-multiplication method, we have        xb1c2−b2c1=yc1a2−a1c2=1a1b2−b1a2⇒    x45−21=y−21−(−15)=1−3−(−9)⇒    x24=y−6=16⇒    x=4 and y=−1

Q.2

(i) For which values of a and b does the following pair of linear equations have an     infinite number of solutions?      2x + 3y =7     (a – b)x + (a + b)y = 3a + b – 2(ii) For which value of k will the following pair of linear equations have no solution?     3x + y = 1    (2k – 1)x + (k – 1) y = 2k + 1

Ans.

(i) Given pair of linear equations are: 2x+3y=7(a−b)x+ (a+b)y=3a+b−2Here,  a1a2=2a−b,   b1b2=3a+b,    c1c2=73a+b−2 For a pair of linear equations to have infinitely many solutions:              a1a2=b1b2=c1c2So, we need         2a−b=3a+b=73a+b−2 or 2a−b=73a+b−2  and    2a−b=3a+bor 2(3a+b−2)=7(a−b) and   2(a+b)=3(a−b)or    6a+2b−4=7a−7b and   2a−3a=−3b−2bor    −a+9b−4=0 and a=5bNow, we put a=5b in  −a+9b−4=0.Thus,         −5b+9b=4 or           4b=4or             b=1Also, a=5b=5×1=5 (ii) Given pair of linear equations are: 3x+y=1(2k−1)x+(k−1)y=2k+1Here,  a1a2=32k−1,   b1b2=1k−1,    c1c2=12k+1 For a pair of linear equations to have no solution:              a1a2=b1b2≠c1c2So, the given pair of linear equations have no solution when         32k−1=1k−1 or 3k−3=2k−1  or 3k−2k=−1+3 or    k=2

Q.3

Solve the following pair of linear equations by thesubstitution and cross-multiplication methods:                    8x+5y=9 3x+2y=4

Ans.

                    8x+5y=9                   ...(1)3x+2y=4                  ...(2)By substitution mwthod:From equation (2), we get                               y=4−3x2Substituting this value of y in equation (1), we get                     8x+5y=9 or                 8x+5×4−3x2=9 or                16x+20−15x=18  or                x=18−20=−2Putting this value of x in equation (2), we get                       3×(−2)+2y=4or −6+2y=4or 2y=4+6=10or y=5 By cross-multiplication method:8x+5y=93x+2y=4Or8x+5y−9=0                   ...(1)3x+2y−4=0                  ...(2)Here, a1= 8, b1= 5, c1=−9a2=3, b2= 2, c2=−4By cross-multiplication method, we have        xb1c2−b2c1=yc1a2−a1c2=1a1b2−b1a2⇒    x−20+18=y−27+32=116−15⇒    x−2=y5=11⇒    x=−2 and y=5

Q.4

Form the pair of linear equations in the followingproblems and find their solutions (if they exist)by any algebraic method: (i) A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay ₹1000 as hostel charges whereas a student B, who takes food for 26 days, pays ₹1180 as hostel charges. Find the fixed charges and the cost of food per day.(ii) A fraction becomes 13 when 1 is subtracted from the numerator and it becomes 14 when 8 is added to its denominator. Find the fraction.(iii) Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?

(iv) Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?(v) The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.

Ans.

(i) Let the fixed charge be ₹x and the cost of food per day be ₹y.According to question,            x+20y=1000               ...(1)and            x+26y=1180  ...(2)Subtracting equation (1) from equation (2), we getx+26y=1180x+20y  =1000−   −         −  ¯          6y=180or y=30Putting this value of y in equation (1), we get          x+20×30=1000or x=1000−600=400Hence, fixed charge is ₹400 and the cost of food perday is ₹30. (ii)Let the fraction be xy.According to question,      x−1y=13    ⇒3x−3=y⇒3x−y=3 ...(1)Also,        xy+8=14⇒ x=y+84⇒ 4x=y+8⇒ 4x−y=8           ...(2)Subtracting equation (2) from equation (1), we get             x=5Substituting this value in equation (1), we get          3×5−y=3or −y=3−15 or y=12Therefore,xy=512Hence, the fraction is 512. (iii) Let the number of right and the number of wronganswers be x and y respectively.According to questions,              3x−y=40                       ...(1)and             4x−2y=50 ⇒         2(2x−y)=2×25⇒         2x−y=25                        ...(2)Subtracting equation (2) from equation (1), we get                x=15Putting this value of x in equation (2), we get             2×15−y=25 ⇒         −y=25−30=−5⇒            y=5Thus,Number of right answers=x=15Number of wrong answers=y=5andNumber of questions=x+y=15+5=20 (iv) Let the speeds of Ist and 2nd cars be x km/h and y km/hrespectively.According to question,              x+y=100                       ...(1)and             5x−100=5y ⇒         5 (x−20)=5y ⇒         x−20=y⇒         x−y=20                          ...(2)Adding equations (1) and (2), we get                2x=120⇒x=60Putting this value of x in equation (1), we get             60+y=100 ⇒         y=100−60=40Thus,Speed of Ist car=x km/h=60  km/hSpeed of 2nd car=y km/h=40 km/h (v)Let length and breadth of the rectangle be x units and y unitsrespectively.According to question,              (x−5)(y+3)=xy−9⇒          xy−5y+3x−15=xy−9    ⇒          −5y+3x=15−9=6⇒             3x−5y−6=0                 ...(1)Also,             (x+3)(y+2)=xy+67 ⇒         xy+3y+2x+6=xy+67 ⇒         3y+2x=67−6=61 ⇒         2x+3y−61=0                     ...(2)By cross-multiplication method, we have               x305−(−18)=y−12−(−183)=19−(−10)⇒          x=32319=17 and y=17119=9Hence, length and breadth of the rectangle are 17 units and9 units respectively.

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FAQs (Frequently Asked Questions)

1. How can students secure higher marks in the CBSE Board Examination of Class 10?

Students of Class 10 can refer to the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5 from the Extramarks website or mobile application. Students are suggested to practice the NCERT exercise problems solutions. They must attempt mock tests and practice sample papers to enhance their preparation. Students may practice sample papers and mock tests based on the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5. They should also refer to the revision notes of the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5. 

2. Why is it recommended to study from the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5 available on Extramarks for the preparation of the CBSE Board Examination of Mathematics?

Extramarks is one of the most reliable educational websites. Extramarks offers top-notch resources and study materials to help students get prepared for examinations. Extramarks offers a variety of educational materials that students can use, including past years’ papers, practice tests, revision material, online live classes, and the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5. Preparing with the help of the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5 can help students perform better in the CBSE board examination.

3. Where can students access study material for the preparation for the Mathematics CBSE Board Examination of Class 10?

The NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5 are available on the Extramarks website and mobile application for students to make use of for their preparation. Students must make sure that they consistently review the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5 to be well-prepared for their CBSE Mathematics examination. It is beneficial for students to regularly and repeatedly practice the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5. Students can use the NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.5 as the primary text to refer to for their preparation.