Exercise 3.5 Class 10 Maths: The NCERT Solutions for Pair of Linear Equations in Two Variables Exercise 3.5 Class 10 Maths is an efficient way to practice for board exams. The questions are provided in an easy to understand manner along with the solutions that will help students prepare for their examination. 

Students must refer to the exercise 3.5 Class 10 Maths NCERT Solutions to improve their preparation. Practicing the NCERT Solutions regularly will help the students identify their weak and strong areas. Therefore, students can work on them simultaneously to improve their understanding of the chapter. Scroll below to find more details about exercise 3.5 Class 10 Maths. 

Exercise 3.5 Class 10 Maths: An Overview

In this section, the students will learn about equations reducible to a pair of linear equations in two variables. The students will get to learn about how to solve equations for pairs that are not linear but can be reduced to a linear format. However, for that, the students must learn about suitable substitutions. 

Exercise 3.5 Class 10 Maths contains important information that will help to verify the details. However, after reducing the pairs, the students must also consider solving the equations to determine if they are verified or not. Different use cases will be introduced to ensure that the students have understood the concepts clearly. 

Students can refer to the exercise 3.5 Class 10 Maths NCERT Solutions so that they can solve their doubts. Nonetheless, students must also have an idea about what are the main contents of CBSE Class 10 chapter 3. 

Given below are the details for CBSE Class 10 that the students must refer to:

Exercise 3.1 Class 10	Pair of Linear Equations in Two Variables
Exercise 3.2 Class 10	Graphical Method of Solution of a Pair of Linear Equations
Exercise 3.3 Class 10	Substitution Method
Exercise 3.4 Class 10	Elimination Method
Exercise 3.5 Class 10	Cross-Multiplication Method
Exercise 3.6 Class 10	Equations Reducible to a Pair of Linear Equations in Two Variables

Exercise 3.5 Class 10 Maths NCERT Solutions: PDF

Students preparing for their Maths exams need to ensure that they follow the exercises properly. Class 10 is one of the most important stages in a student’s life. Therefore, they must prepare for the exam accordingly. 

Pair of linear equations in two variables is a relatively new unit for the students. Although the students have been learning about linear equations from earlier classes, solving the equations among two variables can be slightly difficult for the students. Therefore, they must practice regularly in order to get clarity of concepts. 

Students can refer to the PDFs given below to get their hands on exercise 3.5 Class 10 Maths NCERT Solutions designed by the academic experts at Embibe. The solutions are described in a very efficient manner that will make it easier for the students to prepare for their examinations. 

Students must follow the questions given in the PDF to develop a proper understanding. Now that the students already have an idea about the type of questions that will come in the exam, they must consider referring to all the questions for a better idea. 

(Download Exercise 3.5 Class 10 Maths Solutions from Embibe)

Ex 3.5 Class 10 Maths: About the Exercise

In the previous sections, the students are already made familiar with the calculation of linear equations via different methods. They have studied concepts such as cross-multiplication and more. This has helped to improve their understanding. 

In the given section of exercise 3.5 Class 10 Maths, students will be learning about the equations reducible to a pair of linear equations in two variables. Thus, the section deals with the condition where the equations aren’t linear but after making some changes, the pair of equations is reduced to be linear. 

However, after completing the exercise, it is also necessary to verify whether the reduced expressions have become linear or not. The values can be substituted to determine the successful pair of linear equations. Once the substitution is done, students can use any of the methods described in the previous sections to verify if the equations are linear or not. 

This section can be of great help for the students to understand complex tasks. Once the students understand how the basics of the particular section work, they can also understand how to solve the complex tasks. Practicing the NCERT solutions can be of great help for the students to clarify their concepts. 

Pair of Linear Equations in Two Variables: Chapter Summary

Students have already learnt about linear equations and their pairs in the previous classes. The chapter plays an important role in helping the students clarify their concepts. 

Linear equations in two variables refer to the equations that can be easily expressed as ax+by+c=0 where a, b and c represent real numbers. In the case of this equation, a and b cannot be a zero. The solution of such equations is to find a pair of values for x and y that can be represented on both sides to be equal. 

Class 10 Maths Chapter 3 has seven exercises whereas the last one is an optional one. Once the students are done practicing the chapter, they will learn a lot of new concepts especially with the use of algebraic methods. It is advisable that the students follow each solution closely in order to increase their chances of scoring higher marks in the examination. 

While practicing these questions, the students must remember some important questions. These include:

1. Two linear equations in the same two variables are called a pair of linear equations in two variables. The most general form of a pair of linear equations is a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 where a1, a2, b1, b2, c1, c2 are real numbers. 

2. A pair of linear equations in two variables can be represented, and solved, by the:

(i) graphical method

(ii) algebraic method

3. Algebraic Methods: We have discussed the following methods for finding the solution(s) of a pair of linear equations :

(i) Substitution Method

(ii) Elimination Method

(iii) Cross-multiplication Method

4. Graphical Method: The graph of a pair of linear equations in two variables is represented by two lines.

(i) If the lines intersect at a point, then that point gives the unique solution to the two

equations. In this case, the pair of equations is consistent.

(ii) If the lines coincide, then there are infinitely many solutions — each point on the

line being a solution. In this case, the pair of equations is dependent (consistent).

(iii) If the lines are parallel, then the pair of equations has no solution. In this case, the

a pair of equations is inconsistent.

5. There are several situations which can be mathematically represented by two equations that are not linear to start with. But we alter them so that they are reduced to a pair of linear equations. 

NCERT Solutions for Class 10: Download All-Chapter PDF

Class 10 can be a stepping stone in a student’s life. Therefore, it is advisable that they refer to the proper solutions to boost their learning methods. It is necessary that the students follow the NCERT Solutions for all chapters for better preparation. 

Given below are the download links for the NCERT Solutions for all the Class 10 Maths Chapters. Click on the download links on the table to get the NCERT solutions for. 

Students can click on the download links given in the table to get the NCERT Solutions for Class 10 Maths of all chapters for:

1st Chapter: Real Numbers

2nd Chapter: Polynomials

4th Chapter: Quadratic Equations

5th Chapter: Arithmetic Progressions

6th Chapter: Triangles

7th Chapter: Coordinate Geometry

8th Chapter: Introduction to Trigonometry

9th Chapter: Some Applications of Trigonometry

10th Chapter: Circles

11th Chapter: Constructions

12th Chapter: Areas Related to Circles

13th Chapter: Surface Areas and Volumes

14th Chapter: Statistics

15th Chapter: Probability

Advantages of Referring to NCERT Solutions for Exercise 3.5 Class 10 Maths:

Students preparing for their Class 10 Maths exam need to ensure that they closely follow the NCERT Solutions. Some of the common advantages of referring to the NCERT Solutions include the following:

• The NCERT Solutions are designed by academic experts at Embibe in an easy-to-understand language that can help students get clarity of concepts. 
• Exercise 3.5 Class 10 NCERT Solutions are designed as per the latest NCERT guidelines and revised syllabus of CBSE. 
• Practicing the NCERT Solutions can help students prepare for higher classes and even competitive exams such as IIT, JEE, BITSAT and Olympiad. 
• All the NCERT Solutions are available for. Therefore, students don’t have to worry about spending their money to get access to NCERT Solutions. 
• Since exercise 3.5 Class 10 Maths requires students to have complete clarity, they can turn to NCERT Solutions in case of any doubt. 
• The NCERT Solutions have various practice questions that help students become proficient with the exercises. 

• Students must use the NCERT Solutions for Class 10 wisely to understand the step-wise solution to each question. 
• The NCERT Solutions are designed as per the latest exam syllabus. Therefore, the students will be exposed to the difficulty level. 
• Students must refer to the NCERT Solutions by Embibe as they are authentic and can help them understand what the chapter is all about.

FAQs on Exercise 3.5 Class 10 NCERT Solutions

Students often have certain questions related to Exercise 3.5 Class 10 NCERT Solutions. Therefore, to make it easier for the students, in the section below, we will be asking some of the most frequently asked questions regarding the chapter by students:

Q1: Where can students download the NCERT Solutions for Exercise 3.5 Class 10?
Ans: Students can download the NCERT Solutions for Exercise 3.5 Class 10 Maths for from Embibe. Scroll up to find the download link for the relevant exercises. 

Q2: Are the NCERT Solutions for Exercise 3.5 Maths Class 10 helpful? 
Ans: Students can get significant benefits from scoring better marks in the examination by practicing the NCERT Solutions for Exercise 3.5 Maths Class 10. It is advisable that the students practice these solutions on a regular basis to devise a proper strategy for their exam preparation. 

Q3: Are there any graphical representations? 
Ans: Students practicing the NCERT Solutions for Chapter 3 need to practice the graphical representation as well. Most of the linear equations need to be solved on the graphs. Therefore, referring to them can be extremely efficient for the students to understand what the chapter contains. 

Q4: Do the NCERT Solutions contain the step-by-step solutions for each exercise? 
Ans: Yes. The NCERT Solutions have step-by-step instructions for solving a particular exercise. This further helps the students get a proper clarity regarding how they must solve a particular questions. 

Q5: How many units are there in Chapter 3 Class 10 Solutions? 
Ans: Class 10 Chapter 3 deals with Pair of Linear Equations in Two Variables. There are six units available in the chapter. To excel in their CBSE exams, the students must practice questions from each unit thoroughly. This will play an important role in helping them score better marks in the examination. 

In this article, we have provided you with the download link for NCERT Solutions for Exercise 3.5 Class 10 Maths. Students must practice all the questions from the given PDF thoroughly. It is advisable that the students practice the exercises on their own and refer to the NCERT Solutions only if they get stuck. 

Following this step will help in improving the learning methods of the students. Furthermore, once the students get clarity about a particular unit, they can move to the other ones. Students can also take a mock test for the chapter Pair of Linear Equations in Two Variables for Class 10 from Embibe. This mock test will help students improve their test-taking skills and identify their strong and weak areas. 

Before the exams, students must consider taking the Class 10 mock tests for from Embibe. They can work towards improving their weaker areas and rectify the mistakes that they can potentially make in the real exam. 

We hope our detailed article on NCERT Solutions for Class 10 Maths Exercise 3.5 has been helpful for you. You can download the PDF for the respective units from the links given above. If you have any doubts or queries regarding the solutions, you can drop them in the comments section below. 

Till then, stay tuned to Embibe to receive the latest updates on CBSE exams.