Best and Accurate NCERT Solutions Class 10 Math Chapter 3 Pair of Linear Equations in Two Variables | Maths class 10 ncert solutions | Maths ncert solutions class 10 | 10th class math textbook and solutions | Chapter 3 class 10 maths Solutions
Hey there, Today we will solve all the math's questions from Class 10 Maths NCERT Solutions Chapter 3 Pair of Linear Equations in Two Variables. This Real Number Chapter is most important for your CBSE class 10th Math Examination. So, we provide all the solutions of NCERT Text book for Class 10 Math Chapter 3 "Pair of Linear Equations in Two Variables". Our Pair of Linear Equations in Two Variables Class 10 - NCERT Solutions with PDF article can help you for your many competitive examinations. If you are weak in math, no tension, we are here only for you, we can help you to destroy your fear in mathematics. We use very simple language to teach you this Class 10 NCERT Solutions Maths Chapter 3 - Pair of Linear Equations in Two Variables. Lakhs of students benefit from reading our articles, basically these types of articles. So, guys don't worry, just smile and enjoy our "the best and accurate NCERT Solutions for Class 10 Maths, Chapter 3 Pair of Linear Equations in Two Variables" article . Lets read …….
NCERT Solutions for Class 10 Maths Unit 3
Pair of Linear Equations in Two Variables Class 10
Unit 3 Pair of Linear Equations in Two Variables Exercise 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7 Solutions
If two linear equations have the two same variables, they are called a pair of linear equations in two variables. Following is the most general form of linear equations:
A pair of linear equations
can be represented and solved
by the following methods:
Pair Of Linear Equations In Two Variables Class 10 Ex 3.1 (for CBSE NCERT Class 10 Chapter 3)
Q1 :
A father tells his daughter, “ Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” Represent this situation algebraically and graphically.
Answer :
Let the present age of father be x years and that of daughter = y years
Seven years ago father’s age = (x – 7) years
Seven years ago daughter’s age = (y – 7) years
According to the problem
(x – 7) = 7(y – 7) or x – 7y = – 42 ….(1)
After 3 years father’s age = (x + 3) years
After 3 years daughter’s age = (y + 3) years
According to the condition given in the question
x + 3 = 3(y + 3) or x – 3y = 6 ….(2)
The graphical representation is as follows.
Q2 :
The coach of a cricket team buys 3 bats and 6 balls for Rs 3900. Later, she buys another bat and 3 more balls of the same kind for Rs 1300. Represent this situation algebraically and geometrically.
ANSWER:
Let cost of one bat = Rs x
Cost of one ball = Rs y
3 bats and 6 balls for Rs 3900 So that
3x + 6y = 3900
Dividing equation by 3, we get
x + 3y = 1300
Graphical representation:
we have,
3x + 6y = 3900
3(x + 2y) = 3900
x + 2y = 1300
a = 1300 - 2y
Thus, we have following table:
| x | 1300 | 500 | 700 | 100 |
| y | 0 | 400 | 300 | 600 |
we have, x + 3y = 1300
x = 1300 - 3y
Thus, we have following table:
| x | 1300 | 100 | 400 | 1000 |
| y | 0 | 400 | 300 | 100 |
when we plot the graph of equations, we find that both the lines intersect at the point (1300, 0).
Therefore, a = 1300, y = 0 is the solution of the given system of equations.
The graphical representation for first line is as follows.
Q3 :
The cost of 2 kg of apples and 1 kg of grapes on a day was found to be Rs 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs 300. Represent the situation algebraically and geometrically.
Answer :
Let the cost of 1 kg of apples be Rs x.
And, cost of 1 kg of grapes = Rs y
According to the question, the algebraic representation is
2x + y = 160
4x + 2y = 300
For 2x + y = 160
y = 160 - 2x
The solution table is
x | 50 | 60 | 70 |
y | 60 | 40 | 20 |
For 4x + 2y = 300,
The solution table is
x | 70 | 80 | 75 |
y | 10 | −10 | 0 |
The graphical representation is as follows
Pair Of Linear Equations In Two Variables Class 10 Ex 3.2 (for CBSE NCERT Class 10 Chapter 3)
Q1 :
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 Rs 50, whereas 7 pencils and 5 pens together cost Rs 46. Find the cost of one pencil and that of one pen.
Answer :
(i)
Let the number of girls
be x and the number
of boys be y.
According to the question, the algebraic representation is
x + y = 10
x - y = 4
For
x + y = 10,
x = 10 - y
|
x |
5 |
4 |
6 |
|
y |
5 |
6 |
4 |
For
x - y = 4,
x = 4 + y
|
x |
5 |
4 |
3 |
|
y |
1 |
0 |
- 1 |
Hence, the graphic representation is as follows.
From the figure,
it can be observed that these lines intersect each other at point (7, 3). Therefore, the number of
girls and boys in the class are 7 and 3 respectively.
(ii) Let the cost of 1
pencil be Rs x and the cost of 1
pen be Rs y.
According to the question, the algebraic representation is
5x + 7y = 50
7x + 5y = 46
For 5x + 7y = 50,
|
x |
3 |
10 |
- 4 |
|
y |
5 |
0 |
10 |
7x + 5y = 46
|
x |
8 |
3 |
- 2 |
|
y |
- 2 |
5 |
12 |
Hence, the graphic representation is as follows.
From the figure, it can be observed that these lines intersect each other at point (3, 5).
Therefore, the cost of a
pencil and a pen are Rs 3 and Rs 5 respectively.
Pair Of Linear Equations In Two Variables Class 10 Ex 3.3 (for CBSE NCERT Class 10 Chapter 3)
Pair Of Linear Equations In Two Variables Class 10 Ex 3.4 (for CBSE NCERT Class 10 Chapter 3)
Pair Of Linear Equations In Two Variables Class 10 Ex 3.5 (for CBSE NCERT Class 10 Chapter 3)
Pair Of Linear Equations In Two Variables Class 10 Ex 3.6 (for CBSE NCERT Class 10 Chapter 3)
Pair Of Linear Equations In Two Variables Class 10 Ex 3.7 (for CBSE NCERT Class 10 Chapter 3)
Extra Questions for Class 10 Maths Linear Equations in Two Variables (for CBSE NCERT Class 10 Chapter 3)
NCERT Solutions for Class 10 Mathematics (10th) Chapter 3: Pair of Linear Equations in Two Variables
Concepts covered in Pair of Linear Equations in Two Variables are Concept of Irrational Numbers, Euclid’s Division Lemma, Fundamental Theorem of Arithmetic, Fundamental Theorem of Arithmetic Motivating Through Examples, Introduction of Pair of Linear Equations in Two Variables, Proofs of Irrationality, Rational Numbers and Their Decimal Expansions, Pair of Linear Equations in Two Variables Examples and Solutions.
NCERT Solutions 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 encompasses essential concepts around Pair of Linear Equations in Two Variables such as Euclid’s division lemma, Prime Numbers, Composite Numbers, Fundamental Theorem of Arithmetic, HCF, and LCM by Prime Factorization Method, and Irrational Numbers. Pair of Linear Equations in Two Variables are the combination of rational and irrational numbers. They are denoted by the symbol "R" and can be both positive and negative. NCERT solutions class 10 maths Chapter 3 will help cover all the relevant concepts of Pair of Linear Equations in Two Variables as it has significant applications in real life. Kids also learn about important facts such as the use of the Fundamental Theorem of Arithmetic in proving the irrationality of many of the numbers and exploring when exactly the decimal expansion of a rational number is terminating and when it is non terminating. As numbers form the foundation of Mathematics, understanding the basics is a must.
In this chapter, students will also learn how to represent the Pair of Linear Equations in Two Variables on a number line and the process of successive magnification, which is used to represent a decimal expansion on a number line. The lesson combines certain concepts that kids have come across in previous classes with newer complicated topics to give them a holistic understanding of Pair of Linear Equations in Two Variables and their application. The Class 10 Maths NCERT Solutions Chapter 3 can be found in the pdf format below and also you can find some of these in the exercises given below.
NCERT Solutions for Class 10 Maths Chapter 3 PDF
Mathematics presents us with a variety of numbers and Pair of Linear Equations in Two Variables are one of them. In order to understand higher mathematics, it makes sense to first take a look at the number system in detail which has been achieved in this book. An interesting aspect of the NCERT book is that it details some historical notes, cutting the monotony of studies. Further, the solutions have certain tips and tricks to help a child streamline his process of learning. The links for NCERT Solutions Class 10 Maths available for free PDF download are given below:
Download Class 10 Maths NCERT Solutions Chapter 3 Pair of Linear Equations in Two Variables with PDF and Video Class
Dear Students, Here we provide you the best and accurate Class Ten CBSE NCERT Maths Third Chapter Solutions. Here we also provide you some important video classes and Valuable PDF File, that can help you perform better in your life. Students, you know that this “Pair of Linear Equations in Two Variables” chapter is most important for your examination perpective.
List of Formulas in NCERT Solutions Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables
NCERT solutions Class 10 maths Chapter 3 covers the formulas based on the properties of Pair of Linear Equations in Two Variables and their theorems. These formulas will help the students solve questions accurately and quickly. They are not just helpful for class 10, but higher-level mathematics as well. Apart from these, it is necessary for kids to remember certain points related to a particular category of numbers. For example, the decimal expansion of an irrational number is non-terminating and non-repeating. Let us go through some of the formulas and properties covered in NCERT Solutions Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables.
Important Questions for Class 10 Maths NCERT Solutions Chapter 3
In this “Pair of Linear Equations in Two Variables” chapter many questions are very very important for your exam, so we fully discussed those important questions. In this Third Chapter some more important questions are below, please practice these questions and match your answer with our answer key.
How to solve the NCERT Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables in Easy and Simple way
Hey there, in this article we also cover the easy and best way to solve the CBSE NCERT Class 10 Maths Third Chapter solution. Here we use a different and latest technique of mathematics. Here you can learn the best way to solve math problems. If you have any quarry or questions to us from this Real Number chapter, you can frequently ask your questions, we will try to reply to your questions answer rapidly.
FAQs on NCERT Solutions Class 10 Maths “Pair of Linear Equations in Two Variables” Chapter 3
Many People are like to ask some important and interesting questions from this Pair of Linear Equations in Two Variables chapter. They ask like these types of questions, the questions are the below
- ncert maths class 10 pdf
- Cbse ncert class 10 math solution pdf
- ncert maths book class 10 solutions pdf free download
- ncert solutions for class 10 maths Chapter 3
- class 10 maths book
- ncert class 10 maths text book free pdf download
- Cbse ncert class 10 math solution Chapter 3
- NCERT Solutions for Class 10 Maths: Chapter Wise PDF
- NCERT Solutions for Class 10 Maths CBSE
- Pair of Linear Equations in Two Variables Class 10 - NCERT Solutions with Videos and PDF
Hope you have completed all questions and answers from 10th class Pair of Linear Equations in Two Variables chapter. We have tried our best to answer all the questions from this 10th class Pair of Linear Equations in Two Variables chapter, now the task is for you to study at home. Keep reading, keep practicing, practice makes people better. The more you read, the more you learn, the wiser you become.
You can participate in our quiz for the practice of Pair of Linear Equations in Two Variables chapter of your 10th class, completely free, you can participate in the quiz given below link.
If you want to read more about other chapters of class 10th given below are the chapter wise links, click on the link to read other chapters of class 10th. If you like our service you can follow our website.
