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Class 10 Mathematics Linear Equations Assignments

We have provided below free printable Class 10 Mathematics Linear Equations Assignments for Download in PDF. The Assignments have been designed based on the latest NCERT Book for Class 10 Mathematics Linear Equations . These Assignments for Grade 10 Mathematics Linear Equations cover all important topics which can come in your standard 10 tests and examinations. Free printable Assignments for CBSE Class 10 Mathematics Linear Equations , school and class assignments, and practice test papers have been designed by our highly experienced class 10 faculty. You can free download CBSE NCERT printable Assignments for Mathematics Linear Equations Class 10 with solutions and answers. All Assignments and test sheets have been prepared by expert teachers as per the latest Syllabus in Mathematics Linear Equations Class 10. Students can click on the links below and download all Pdf Assignments for Mathematics Linear Equations class 10 for free. All latest Kendriya Vidyalaya Class 10 Mathematics Linear Equations Assignments with Answers and test papers are given below.

Mathematics Linear Equations Class 10 Assignments Pdf Download

We have provided below the biggest collection of free CBSE NCERT KVS Assignments for Class 10 Mathematics Linear Equations . Students and teachers can download and save all free Mathematics Linear Equations assignments in Pdf for grade 10th. Our expert faculty have covered Class 10 important questions and answers for Mathematics Linear Equations as per the latest syllabus for the current academic year. All test papers and question banks for Class 10 Mathematics Linear Equations and CBSE Assignments for Mathematics Linear Equations Class 10 will be really helpful for standard 10th students to prepare for the class tests and school examinations. Class 10th students can easily free download in Pdf all printable practice worksheets given below.

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Advantages of Class 10 Mathematics Linear Equations Assignments

• As we have the best and largest collection of Mathematics Linear Equations assignments for Grade 10, you will be able to easily get full list of solved important questions which can come in your examinations.
• Students will be able to go through all important and critical topics given in your CBSE Mathematics Linear Equations textbooks for Class 10 .
• All Mathematics Linear Equations assignments for Class 10 have been designed with answers. Students should solve them yourself and then compare with the solutions provided by us.
• Class 10 Students studying in per CBSE, NCERT and KVS schools will be able to free download all Mathematics Linear Equations chapter wise worksheets and assignments for free in Pdf
• Class 10 Mathematics Linear Equations question bank will help to improve subject understanding which will help to get better rank in exams

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You can click on the links above and get assignments for Mathematics Linear Equations in Grade 10, all topic-wise question banks with solutions have been provided here. You can click on the links to download in Pdf.

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Chapter 3 Class 10 Pair of Linear Equations in Two Variables

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Get NCERT solutions of Chapter 3 Class 10 - Pair of Linear Equations in Two Variables at Teachoo. Answers to all exercise questions, examples and optional questions have been provided with video of each and every question

We studied  Linear Equations in Two Variables in Class 9, we will study pair of linear equations in this chapter.

In this chapter, we will learn

• What are Linear Equations in Two Variables
• Converting statements into Equations , and drawing graph of those linear equations
• Possible Type of Graphs for Pair of Linear Equations in Two Variables - Two Lines Intersecting, Two lines Parallel, Coincident Lines
• Finding s olution of equations from graphs
• Consistency of equations  by finding ratio of a 1 /a 2 , b 1 /b 2 , c 1 /c 2
• Intersecting Lines (Exactly one solution - unique)
• Coincident Lines (Infinitely many solutions)
• Parallel Lines ( No solutions)
• Substitution Method
• Elimination Method
• Cross Multiplication Method
• Solving complicated equations like 2/x + 3/y = 4 by substituting variables (like putting p = 1/x, q = 1/y and solving)
• Solving Statement Questions by first forming equations, and then solving

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

NCERT solutions for class 10 maths chapter 3 Pair of Linear Equations in Two Variables enables the students to understand and explore simple ways to solve linear equations. This is a chapter that is widely used in industrial applications. It is used to solve questions based on speed-distance, money percentage, age, force-pressure, and so on. The kids will cover algebraic methods of solving a pair of linear equations in two variables, like the elimination method, the cross-multiplication method, and equations reducible to a pair of linear equations in two variables.

The NCERT solutions class 10 maths chapter 3 Pair of Linear Equations in Two Variables teaches that the general form of a linear equation in two variables is ax + by + c = 0, where x and y are variables and a, b and c are real numbers. Now, in this equation, the constants with variables cannot be equal to zero simultaneously. Such equations have two values, each for ‘x’ and ‘y’, which make both sides of the equation equal. The class 10 maths NCERT solutions chapter 3 Pair of linear equations in two variables can be accessed through the links below and also you can find some of these in the exercises given below.

• NCERT Solutions Class 10 Maths Chapter 3 Ex 3.1
• NCERT Solutions Class 10 Maths Chapter 3 Ex 3.2
• NCERT Solutions Class 10 Maths Chapter 3 Ex 3.3
• NCERT Solutions Class 10 Maths Chapter 3 Ex 3.4
• NCERT Solutions Class 10 Maths Chapter 3 Ex 3.5
• NCERT Solutions Class 10 Maths Chapter 3 Ex 3.6
• NCERT Solutions Class 10 Maths Chapter 3 Ex 3.7

NCERT Solutions for Class 10 Maths Chapter 3 PDF

Linear equations are implemented to overcome real-world problems in a variety of fields. To evaluate this type of equation, we must either apply the substitution technique or mathematical elimination, which is explained with appropriate examples in the NCERT solutions class 10 maths chapter 3 Pair of linear equations in two variables. The pdf of the different exercises in the chapter can be found below :

☛ Download Class 10 Maths NCERT Solutions Chapter 3

NCERT Class 10 Maths Chapter 3   Download PDF

A linear equation in two variables can also be easily represented on a graph. Since the equation forms a straight line , and a line can have infinitely many solutions so each solution can be uniquely plotted on the graph . Equations aren't simply a theoretical concept; they're also incredibly useful in everyday situations; hence, it is essential that the students get a practical problem-solving approach with the help of the examples and questions presented in the chapter. A section-wise quick analysis of the exercise questions in the NCERT Solutions Class 10 Maths Chapter 3 Pair Of Linear Equations In Two Variables can be seen below :

• Class 10 Maths Chapter 3 Ex 3.1 - 3 Questions
• Class 10 Maths Chapter 3 Ex 3.2 - 7 Questions
• Class 10 Maths Chapter 3 Ex 3.3 - 3 Questions
• Class 10 Maths Chapter 3 Ex 3.4 - 2 Questions
• Class 10 Maths Chapter 3 Ex 3.5 - 4 Questions
• Class 10 Maths Chapter 3 Ex 3.6 - 2 Questions
• Class 10 Maths Chapter 3 Ex 3.7 - 8 Questions

Topics Covered: The topics covered in class 10 maths NCERT Solutions chapter 3 include the definition of linear equations, graphical method of a solution of a pair of linear equations, algebraic methods of solving a pair of linear equations by elimination, substitution, and cross multiplication , as well as equations reducible to a pair of linear equations.

Total Questions: Class 10 maths chapter 3 Pair Of Linear Equations In Two Variables consists of 29 questions, of which 12 are long answers, 8 are moderate-level, and 9 are easy problems. These sums are solved in a step-wise manner so that students can get a conceptual understanding of the topics covered in this chapter.

List of Formulas in NCERT Solutions Class 10 Maths Chapter 3

Formulas give a way to simplify a tough sum and solve it more efficiently. A pair of linear equations can be solved using two methods, one is the algebraic method, and the other is the graphical method. In order to use these techniques, we need to cover topics such as the standard form of linear equations, equations for simultaneous pairs, etc. It is advised that kids make a formula chart that outlines the steps needed to be used when attempting such problems. This also helps them to revise the chapter at a steady pace and efficiently. Some of the important equations from this chapter of NCERT Solutions have been mentioned below:

• Pair of linear equations in two variables :

x = a 1 x + b 1 y + c 1 = 0 : y = a 2 x + b 2 y + c 2 = 0

The above two equations signify the general form of a system of linear equations that can be solved using elimination and substitution methods.

• Cross Multiplication Method : If a pair of linear equations given by a 1 x + b 1 y + c 1 = 0 and a 2 x + b 2 y + c 2 = 0, then the following conditions are possible :
• a 1 /a 2 ≠ b 1 /b 1 : depicting consistent pair of linear equations
• a 1 /a 2 = b 1/ b 2 ≠ c 1/ c 2 : depicting inconsistent pair of linear equations
• a 1 /a 2 = b 1 /b 2 = c 1 /c 2 : depicting dependent as well as consistent pair of linear equations

Important Questions for Class 10 Maths NCERT Solutions Chapter 3

Video solutions for class 10 maths ncert chapter 3, faqs on ncert solutions class 10 maths chapter 3, why are ncert solutions class 10 maths chapter 3 vital for scoring well.

NCERT solutions class 10 maths chapter 3 have been prepared by experts and provide practical and graphical methods of solving a pair of linear equations with examples. The important topics such as consistent, inconsistent, and dependent pair of equations in two variables are explained in a step-wise manner with appropriate examples. Also, the CBSE board recommends studying NCERT solutions making them a vital resource.

Do I Need to Practice all Questions Given in Class 10 Maths NCERT Solutions Linear Equations in Two Variables?

The NCERT solutions class 10 maths linear equations in two variables have examples and exercise questions that cover the important topics in detail and will help to build a strong foundation for students. The set of questions cover both algebraic and graphical problems. The more kids will practice all the problems, the better clarity they will get on the concepts. Hence, it's essential that the students aim to solve all the questions.

What are the Important Topics Covered in NCERT Solutions Class 10 Maths Chapter 3?

The important topics covered in the NCERT solutions class 10 maths chapter 3 are the definition of a linear equation, degrees of an equation, as well as the elimination and substitution method. NCERT solutions help the students learn how to multiply the equations. They will also come across new terms like consistent, inconsistent pair of linear equations, point of intersection, and many more.

How Many Questions are there in Class 10 Maths NCERT Solutions Chapter 3?

The NCERT Solutions contain a total of 29 well-researched questions that include both graph-based as well as algebraic sums. These 29 questions are distributed across 7 exercises. Students must go through all the examples before solving these exercises. Each question has been solved in a detailed manner with appropriate explanations in the NCERT solutions class 10 maths chapter 3.

What are the Important Formulas in NCERT Solutions Class 10 Maths Chapter 3?

The important formulas mentioned in the NCERT Solutions class 10 maths chapter 3 are formulas for the cross-multiplication and division methods. Students must also remember the standard form of linear equations in two variables, as well as their general equations. These formulas are very important from an exam perspective and can help students solve questions in minutes. In order to understand the derivation of these formulas, kids must go through the theory of the chapter.

Why Should I Practice NCERT Solutions Class 10 Maths Chapter 3?

NCERT solutions focus on equations reducible to a pair of linear equations in two variables. Practicing the elimination and substitution methods will help students master NCERT solutions class 10 maths chapter 3. Questions related to these topics are frequently asked in board exams hence it is important to go through these solutions on a regular basis in order to score excellent marks.

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

In Class 10 Maths Chapter 3 NCERT solutions, which typically covers topics related to Pair of Linear Equations in Two Variables, we will learn to solve a set of linear equations. This chapter introduces students to the concept of solving a system of two linear equations with two variables. Here are the main points to study in this chapter. Exercises of Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables There are only three exercises, exercise 3.1, 3.2 and 3.3 in course for academic session 2024-25 exams. Learn how to determine whether a pair of linear equations has a unique solution, no solution, or infinitely many solutions.

Class 10 Maths Exercise 3.1 Learn how to represent a pair of linear equations graphically on the Cartesian plane and understand how to find the solution (if any) by finding the point of intersection. Study different methods for solving a pair of linear equations algebraically.

Class 10 Maths Exercise 3.2 Solve one equation for one variable and substitute it into the other equation. Explore real-world applications of pair of linear equations, such as problems involving age, numbers, and consecutive natural numbers. Understand the concepts of consistent, inconsistent, and dependent systems of linear equations.

Class 10 Maths Exercise 3.3 Add or subtract the equations to eliminate one variable and solve for the other. Learn how to convert certain types of problems in a pair of linear equations and solve them using the methods mentioned above. Practice solving word problems related to pair of linear equations by converting the given information into equations and solving them.

Previous Chapter: Chapter 2 Polynomials Next Chapter: Chapter 4 Quadratic Equations Class 10 Maths all Chapter’s Solutions

Utilize online resources available at Tiwari Academy website, Android and iOS Apps , video tutorials, and interactive practice platforms to enhance your learning experience and access additional practice problems. By following these tips and putting in consistent effort, you can practice Class 10 Maths Chapter 3 effectively and improve your chances of scoring well in your board exams.

Practicing Class 10 Maths Chapter 3 , which is about linear equations in two variables, is crucial for achieving a good score in your CBSE board exams. Here are some effective tips on how to practice this chapter. Before you start practicing, make sure you have a clear understanding of the concepts related to linear equations. Read the chapter thoroughly and pay attention to definitions, formulas, and examples.

Start with the exercises provided in your NCERT textbook. Work through each question step by step. Ensure that you understand the logic behind each solution rather than just memorizing the steps.

Consistent practice is key to mastering in class 10 mathematics chapter 3 . Set aside a specific time each day to practice linear equations. The more you practice, the more confident you’ll become in solving different types of problems. Don’t limit yourself to the textbook exercises.

Look for additional resources, such as sample papers, previous year’s question papers, and online practice materials, to solve a variety of problems. This will help you become proficient in tackling different types of questions. Linear equations are often presented as word problems. Practice solving real-life scenarios where linear equations are used to model and solve problems. This will help you develop problem-solving skills.

Linear equations in two variables can be represented graphically as lines on a coordinate plane. Practice plotting and interpreting these graphs of questions given in 10th Maths Exercise 3.1. Understand how to find solutions graphically as well. Review what you’ve learned on a regular basis. Go back to previously solved problems and try solving them again to reinforce your understanding.

If you encounter difficulties with specific topics or problems, don’t hesitate to ask your teacher for clarification or seek help from a tutor or classmates.

As your exams approach, practice full-length mock tests. Time yourself to simulate exam conditions. This will help you improve your time management skills and reduce exam anxiety. Whenever you make a mistake, take the time to understand where you went wrong.

Analyze your errors, learn from them, and avoid making the same mistakes in the future. Maintaining a positive attitude and staying calm during your preparation and exams is essential. Believe in your abilities and stay confident.

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Assignments Class 10 Mathematics Linear Equations Pdf Download

Students can refer to Assignments for Class 10 Mathematics Linear Equations available for download in Pdf. We have given below links to subject-wise free printable Assignments for Mathematics Linear Equations Class 10 which you can download easily. All assignments have a collection of questions and answers designed for all topics given in your latest NCERT Books for Class 10 Mathematics Linear Equations for the current academic session. All Assignments for Mathematics Linear Equations Grade 10 have been designed by expert faculty members and have been designed based on the type of questions asked in standard 10 class tests and exams. All Free printable Assignments for NCERT CBSE Class 10, practice worksheets, and question banks have been designed to help you understand all concepts properly. Practicing questions given in CBSE NCERT printable assignments for Class 10 with solutions and answers will help you to further improve your understanding. Our faculty have used the latest syllabus for Class 10. You can click on the links below to download all Pdf assignments for class 10 for free. You can get the best collection of Kendriya Vidyalaya Class 10 Mathematics Linear Equations assignments and questions workbooks below.

Class 10 Mathematics Linear Equations Assignments Pdf Download

CBSE NCERT KVS Assignments for Mathematics Linear Equations Class 10 have been provided below covering all chapters given in your CBSE NCERT books. We have provided below a good collection of assignments in Pdf for Mathematics Linear Equations standard 10th covering Class 10 questions and answers for Mathematics Linear Equations. These practice test papers and workbooks with question banks for Class 10 Mathematics Linear Equations Pdf Download and free CBSE Assignments for Class 10 are really beneficial for you and will support in preparing for class tests and exams. Standard 10th students can download in Pdf by clicking on the links below.

Subjectwise Assignments for Class 10 Mathematics Linear Equations

Benefits of Solving Class 10 Mathematics Linear Equations Assignments

• The best collection of Grade 10 assignments for Mathematics Linear Equations have been provided below which will help you in getting better marks in class tests and exams.
• The solved question for Class 10 Mathematics Linear Equations will help you to gain more confidence to attempt all types of problems in exams
• Latest NCERT Books for Class 10 Mathematics Linear Equations have been referred to for designing these assignments
• We have provided step by step solutions for all questions in the Class 10 assignments so that you can understand the solutions in detail.
• We have provided single click download links to all chapterwise worksheets and assignments in Pdf.
• Class 10 practice question banks will support to enhance subject knowledge and therefore help to get better marks in exam

FAQs by Mathematics Linear Equations Students in Class 10

At https://www.ncertbooksolutions.com is the best website that has the biggest collection of free printable assignments for Class 10 Mathematics Linear Equations.

We provide here Standard 10 subject-wise assignments which can be easily downloaded in Pdf format for free. Our teachers have provided these Grade 10 Mathematics Linear Equations test sheets for Mathematics Linear Equations given in your books.

You can click on the links above and get assignments for Mathematics Linear Equations in Grade 10, all chapters and topic-wise question banks with solutions have been provided here. You can click on the links to download in Pdf.

We have provided here subject-wise Grade 10 Mathematics Linear Equations question banks, revision notes and questions for all difficult topics, and other study material. You can download it all without any charge by clicking on the links provided above.

We have provided the best quality question bank for Class 10 for Mathematics Linear Equations available for Pdf Download. You can download them all and use them offline without the internet.

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

• Exercise 3.1
• Exercise 3.2
• Exercise 3.3
• Exercise 3.4
• Exercise 3.5
• Exercise 3.6
• Exercise 3.7

NCERT Solutions for Class 10 Maths Chapters:

How many exercises in chapter 3 pair of linear equations in two variables, at a certain time in a deer park, the number of heads and the number of legs of deer and human visitors were counted and it was found there were 39 heads & 132 legs. find the number of deer and human visitors in the park., what is graphical method of solution of a pair of linear equations, when the son will be as old as the father today their ages will add up to 126 years. when the father was old as the son is today, their ages add upto 38 years. find their present ages., contact form.

• NCERT Solutions
• NCERT Solutions for Class 10
• NCERT Solutions for Class 10 Maths
• Chapter 3: Linear Equations In Two Variables
• Exercise 3.2

NCERT Solutions for Class 10 Maths Chapter 3 - Pair of Linear Equations in Two Variables Exercise 3.2

NCERT Solutions for Class 10 Maths Exercise 3.2 Chapter 3 Linear Equations In Two Variables is the best way students can prepare the concept. These NCERT Solutions have all the solutions to the questions provided in the exercise on page no. 73. The answers provided by our subject experts are accurate and have been prepared after a lot of brainstorming.

Solutions to all the exercises mentioned in the textbook are provided in the NCERT Solutions of Class 10 Maths. It also contains several other questions for practice. These questions will help the students prepare well for the board examinations. NCERT Class 10 Maths Solutions Chapter 3 – Pair of Linear Equations in Two Variables is an important chapter from the examination perspective. The students need to be thorough with the basic concepts to solve the problems related to this chapter.

Solutions of NCERT act as a guide during preparation for the examinations. The students can refer to them in case of any doubts. They can practise and evaluate themselves and work on their weak points thereafter.

• Chapter 1 Real Numbers
• Chapter 2 Polynomials
• Chapter 3 Pair of Linear Equations in Two Variables
• Chapter 4 Quadratic Equations
• Chapter 5 Arithmetic Progressions
• Chapter 6 Triangles
• Chapter 7 Coordinate Geometry
• Chapter 8 Introduction to Trigonometry
• Chapter 9 Some Applications of Trigonometry
• Chapter 10 Circles
• Chapter 11 Constructions
• Chapter 12 Areas Related to Circles
• Chapter 13 Surface Areas and Volumes
• Chapter 14 Statistics
• Chapter 15 Probability
• Exercise 3.1 Chapter 3 Pair of Linear Equations in Two Variables
• Exercise 3.2 Chapter 3 Pair of Linear Equations in Two Variables
• Exercise 3.3 Chapter 3 Pair of Linear Equations in Two Variables
• Exercise 3.4 Chapter 3 Pair of Linear Equations in Two Variables
• Exercise 3.5 Chapter 3 Pair of Linear Equations in Two Variables
• Exercise 3.6 Chapter 3 Pair of Linear Equations in Two Variables
• Exercise 3.7 Chapter 3 Pair of Linear Equations in Two Variables

Download PDF for NCERT Solutions Class 10 Maths Chapter 3 – Pair of Linear Equations in Two Variables Exercise 3.2

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NCERT Solutions for Class 10 Maths Chapter 3 – Pair of Linear Equations in Two Variables Exercise 3.2

1. Form the pair of linear equations in the following problems, and find their solutions graphically.

(i) 10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.

(ii) 5 pencils and 7 pens together cost 50, whereas 7 pencils and 5 pens together cost 46. Find the cost of one pencil and that of one pen.

(i) Let there be x number of girls and y number of boys. As per the given question, the algebraic expression can be represented as follows.

Now, for x+y = 10 or x = 10−y, the solutions are;

For x – y = 4 or x = 4 + y, the solutions are;

The graphical representation is as follows;

From the graph, it can be seen that the given lines cross each other at point (7, 3). Therefore, there are 7 girls and 3 boys in the class.

(ii) If 1 pencil costs Rs. x and 1 pen costs Rs. y.

According to the question, the algebraic expression cab be represented as;

5x + 7y = 50

7x + 5y = 46

For, 5x + 7y = 50 or  x = (50-7y)/5, the solutions are;

For 7x + 5y = 46 or x = (46-5y)/7, the solutions are;

Hence, the graphical representation is as follows;

From the graph, it is can be seen that the given lines cross each other at point (3, 5).

So, the cost of a pencil is 3/- and cost of a pen is 5/-.

2. On comparing the ratios a1/a2 , b1/b2 , c1/c2, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident:

(i) 5x – 4y + 8 = 0

7x + 6y – 9 = 0

(ii) 9x + 3y + 12 = 0

18x + 6y + 24 = 0

(iii) 6x – 3y + 10 = 0

2x – y + 9 = 0

(i) Given expressions;

5x−4y+8 = 0

7x+6y−9 = 0

Comparing these equations with a1x+b1y+c1 = 0

And a2x+b2y+c2 = 0

a1 = 5, b1 = -4, c1 = 8

a2 = 7, b2 = 6, c2 = -9

(a1/a2) = 5/7

(b1/b2) = -4/6 = -2/3

(c1/c2) = 8/-9

Since, (a1/a2) ≠ (b1/b2)

So, the pairs of equations given in the question have a unique solution and the lines cross each other at exactly one point.

(ii) Given expressions;

9x + 3y + 12 = 0

a1 = 9, b1 = 3, c1 = 12

a2 = 18, b2 = 6, c2 = 24

(a1/a2) = 9/18 = 1/2

(b1/b2) = 3/6 = 1/2

(c1/c2) = 12/24 = 1/2

Since (a1/a2) = (b1/b2) = (c1/c2)

So, the pairs of equations given in the question have infinite possible solutions and the lines are coincident.

(iii) Given Expressions;

6x – 3y + 10 = 0

a1 = 6, b1 = -3, c1 = 10

a2 = 2, b2 = -1, c2 = 9

(a1/a2) = 6/2 = 3/1

(b1/b2) = -3/-1 = 3/1

(c1/c2) = 10/9

Since (a1/a2) = (b1/b2) ≠ (c1/c2)

So, the pairs of equations given in the question are parallel to each other and the lines never intersect each other at any point, and there is no possible solution for the given pair of equations.

3. On comparing the ratio, (a1/a2) , (b1/b2) , (c1/c2), find out whether the following pair of linear equations are consistent, or inconsistent.

(i) 3x + 2y = 5 ; 2x – 3y = 7

(ii) 2x – 3y = 8 ; 4x – 6y = 9

(iii)(3/2)x+(5/3)y = 7; 9x – 10y = 14

(iv) 5x – 3y = 11 ; – 10x + 6y = –22

(v)(4/3)x+2y = 8 ; 2x + 3y = 12

(i) Given : 3x + 2y = 5 or 3x + 2y -5 = 0

and 2x – 3y = 7 or 2x – 3y -7 = 0

Comparing these equations with a1x+b1y+c1 = 0

a1 = 3, b1 = 2, c1 = -5

a2 = 2, b2 = -3, c2 = -7

(a1/a2) = 3/2

(b1/b2) = 2/-3

(c1/c2) = -5/-7 = 5/7

So, the given equations intersect each other at one point and they have only one possible solution. The equations are consistent.

(ii) Given 2x – 3y = 8 and 4x – 6y = 9

a1 = 2, b1 = -3, c1 = -8

a2 = 4, b2 = -6, c2 = -9

(a1/a2) = 2/4 = 1/2

(b1/b2) = -3/-6 = 1/2

(c1/c2) = -8/-9 = 8/9

Since , (a1/a2) = (b1/b2) ≠ (c1/c2)

So, the equations are parallel to each other and they have no possible solution. Hence, the equations are inconsistent.

(iii) Given (3/2)x + (5/3)y = 7 and 9x – 10y = 14

a1 = 3/2, b1 = 5/3, c1 = -7

a2 = 9, b2 = -10, c2 = -14

(a1/a2) = 3/(2×9) = 1/6

(b1/b2) = 5/(3× -10)= -1/6

(c1/c2) = -7/-14 = 1/2

So, the equations are intersecting  each other at one point and they have only one possible solution. Hence, the equations are consistent.

(iv) Given, 5x – 3y = 11 and – 10x + 6y = –22

a1 = 5, b1 = -3, c1 = -11

a2 = -10, b2 = 6, c2 = 22

(a1/a2) = 5/(-10) = -5/10 = -1/2

(b1/b2) = -3/6 = -1/2

(c1/c2) = -11/22 = -1/2

These linear equations are coincident lines and have infinite number of possible solutions. Hence, the equations are consistent.

(v) Given, (4/3)x +2y = 8 and 2x + 3y = 12

a1 = 4/3 , b1= 2 , c1 = -8

a2 = 2, b2 = 3 , c2 = -12

(a1/a2) = 4/(3×2)= 4/6 = 2/3

(b1/b2) = 2/3

(c1/c2) = -8/-12 = 2/3

4. Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:

(i) x + y = 5, 2x + 2y = 10

(ii) x – y = 8, 3x – 3y = 16

(iii) 2x + y – 6 = 0, 4x – 2y – 4 = 0

(iv) 2x – 2y – 2 = 0, 4x – 4y – 5 = 0

(i) Given, x + y = 5 and 2x + 2y = 10

(a1/a2) = 1/2

(b1/b2) = 1/2

(c1/c2) = 1/2

∴ The equations are coincident and they have infinite number of possible solutions.

So, the equations are consistent.

For, x + y = 5 or x = 5 – y

For 2x + 2y = 10 or x = (10-2y)/2

So, the equations are represented in graphs as follows:

From the figure, we can see, that the lines are overlapping each other.

Therefore, the equations have infinite possible solutions.

(ii) Given, x – y = 8 and 3x – 3y = 16

(a1/a2) = 1/3

(b1/b2) = -1/-3 = 1/3

(c1/c2) = 8/16 = 1/2

Since, (a1/a2) = (b1/b2) ≠ (c1/c2)

The equations are parallel to each other and have no solutions. Hence, the pair of linear equations is inconsistent.

(iii) Given, 2x + y – 6 = 0 and 4x – 2y – 4 = 0

(a1/a2) = 2/4 = ½

(b1/b2) = 1/-2

(c1/c2) = -6/-4 = 3/2

The given linear equations are intersecting each other at one point and have only one solution. Hence, the pair of linear equations is consistent.

Now, for 2x + y – 6 = 0 or y = 6 – 2x

And for 4x – 2y – 4 = 0 or y = (4x-4)/2

From the graph, it can be seen that these lines are intersecting each other at only one point (2,2).

(iv) Given, 2x – 2y – 2 = 0 and 4x – 4y – 5 = 0

(b1/b2) = -2/-4 = 1/2

(c1/c2) = 2/5

Since, a1/a2 = b1/b2 ≠ c1/c2

Thus, these linear equations have parallel and have no possible solutions. Hence, the pair of linear equations are inconsistent.

5. Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.

Solutions: Let us consider.

The width of the garden is x and length is y.

Now, according to the question, we can express the given condition as;

Now, taking y – x = 4 or y = x + 4

For y + x = 36, y = 36 – x

The graphical representation of both the equation is as follows;

From the graph you can see, the lines intersect each other at a point (16, 20). Hence, the width of the garden is 16 and length is 20.

6. Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is:

(i) Intersecting lines

(ii) Parallel lines

(iii) Coincident lines

(i) Given the linear equation 2x + 3y – 8 = 0.

To find another linear equation in two variables such that the geometrical representation of the pair so formed is intersecting lines, it should satisfy the below condition;

(a1/a2) ≠ (b1/b2)

Thus, another equation could be 2x – 7y + 9 = 0, such that;

(a1/a2) = 2/2 = 1 and (b1/b2) = 3/-7

Clearly, you can see another equation satisfies the condition.

(ii) Given the linear equation 2x + 3y – 8 = 0.

To find another linear equation in two variables such that the geometrical representation of the pair so formed is parallel lines, it should satisfy the below condition;

(a1/a2) = (b1/b2) ≠ (c1/c2)

Thus, another equation could be 6x + 9y + 9 = 0, such that;

(a1/a2) = 2/6 = 1/3

(b1/b2) = 3/9= 1/3

(c1/c2) = -8/9

(iii) Given the linear equation 2x + 3y – 8 = 0.

To find another linear equation in two variables such that the geometrical representation of the pair so formed is coincident lines, it should satisfy the below condition;

(a1/a2) = (b1/b2) = (c1/c2)

Thus, another equation could be 4x + 6y – 16 = 0, such that;

(a1/a2) = 2/4 = 1/2 ,(b1/b2) = 3/6 = 1/2, (c1/c2) = -8/-16 = 1/2

7. Draw the graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.

Solution: Given, the equations for graphs are x – y + 1 = 0 and 3x + 2y – 12 = 0.

For, x – y + 1 = 0 or x = -1+y

For, 3x + 2y – 12 = 0 or x = (12-2y)/3

Hence, the graphical representation of these equations is as follows;

From the figure, it can be seen that these lines are intersecting each other at point (2, 3) and x-axis at (−1, 0) and (4, 0). Therefore, the vertices of the triangle are (2, 3), (−1, 0), and (4, 0).

This is the second exercise of the chapter. It has a total of 7 questions. The solutions to these questions are provided in NCERT Solutions for Class 10 Maths Chapter 3 – Pair of Linear Equations in Two Variables Exercise 3.2. The students can refer to this page for solutions. The solutions are provided stepwise by the subject experts and are accurate.

Key Features of NCERT Solutions Class 10 Maths Chapter 3 – Pair of Linear Equations in Two Variables Exercise 3.2

• The questions are solved by subject experts.
• The answers are provided after a lot of brainstorming and are accurate.
• These will help in scoring well in the examinations.
• NCERT Solutions Class 10 Maths Chapter 3 – Pair of Linear Equations in Two Variables includes the solutions to the exercises given in the textbook.

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