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NCERT Solutions for Exercise 3.1 Class 10 Maths Chapter 3 - Pair of Linear Equations in two variables

NCERT Solutions for Exercise 3.1 Class 10 Maths Chapter 3 - Pair of Linear Equations in two variables

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CBSE Class 10th Exam Date:01 Jan' 26 - 14 Feb' 26

#CBSE Class 10th
Ramraj SainiUpdated on 08 Nov 2023, 07:42 PM IST

NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1

NCERT Solutions for class 10 maths ex 3.1 Pair of Linear Equations in two variables is discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the latest syllabus and pattern of CBSE 2023-24. This ex 3.1 class 10 deals with the graphical and algebraic representations of linear equations in two variables and their different type of solutions such as a unique solution, no solutions or infinitely many solutions, using the five methods namely the Graphical method, substitution method, cross Multiplication method, elimination method and determinant method.

These class 10 maths ex 3.1 solutions are designed as per the students demand covering comprehensive, step by step solutions of every problems. Practice these questions and answers to command the concepts, boost confidence and in depth understanding of concepts. Students can find all exercise together using the link provided below.

Download PDF of NCERT Solutions For Class 10 Maths Chapter 1 Exercise 3.1

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Access Exercise 3.1 Class 10 Maths Answers

Pair of Linear Equations in Two Variables Class 10 Chapter 3 Excercise: 3.1

Q1 Aftab 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.” (Isn’t this interesting?) Represent this situation algebraically and graphically.

Answer: Let x be the age of Aftab and y be the age of his daughter

Now, According to the question,

$(x-7)=7\times(y-7)$

$\Rightarrow x-7=7y-49$

$\Rightarrow x-7y=-42.....(1)$

Also,

$(x+3)=3(y+3)$

$\Rightarrow x+3=3y+9$

$\Rightarrow x-3y=6.....(2)$

Now, let's represent both equations graphically,

From (1), we get

$y=\frac{x+42}{7}$

So, Putting different values of x we get corresponding values of y

X
0
7
-7
Y
6
7
5


And From (2) we get,

$y=\frac{x-6}{3}$

So, Putting different values of x we get corresponding values of y

X
0
3
6
Y
-2
-1
0

GRAPH:

Graph X-Y

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 the price of one Bat be x and the price of one ball be y,

Now, According to the question,

$3x+6y=3900.....(1)$

$x+3y=1300.....(2)$

From(1) we have

$y=\frac{3900-3x}{6}$

By putting different values of x, we get different corresponding values of y.So

X
100
300
-100
Y
600
500
700

Now, From (2), we have,

$y=\frac{1300-x}{3}$

By putting different values of x, we get different corresponding values of y.So

X
100
400
-200
Y
400
300
500

GRAPH:

1635919652158

Q3 The cost of 2 kg of apples and 1kg 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, x be the cost of 1kg apple and y be the cost of 1kg grapes.

Now, According to the question,

On a day:

$2x+y=160.....(1)$

After One Month:

$4x+2y=300.....(2)$

Now, From (1) we have

$y=160-2x$

Putting different values of x we get corresponding values of y, so,'

X
80
60
50
Y
0
40
60


And From (2) we have,

$y=\frac{300-4x}{2}=150-2x$

Putting different values of x we get corresponding values of y, so,

X
50
60
70
Y
50
30
10

Graph:

graph

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More About NCERT Solutions for Class 10 Maths Exercise 3.1

10th class maths exercise 3.1 answers – Consists of 3 simple questions in word problem format. In exercise 3.1 Class 10 Maths, If the system of equations is consistent and independent, then they have a unique solution and their condition is a1/a2 not equal to b1/b2 . Also if the system of equations is inconsistent and independent, then there will be no solution and their condition is a1/a2 = b1/b2 not equal to c1/c2 . Similarly, If the system of equations is consistent and dependent, then they have an infinite number of solutions and their condition is a1/a2 = b1/b2 = c1/c2 . The NCERT solutions for Class 10 Maths exercise 3.1 mainly focused on the graphical representation of the system of equations. All the three questions related to the graphical representation are given in exercise 3.1 Class 10 Maths. Also students can get access of Pair of linear equations in two variables notes to revise all the concepts discussed in this chapter.

Benefits of NCERT Solutions for Class 10 Maths Exercise 3.1

• NCERT solutions for Class 10 Maths is considered the best material for solving Class 10 Maths chapter 3 exercise 3.1 also assists us in solving and revising all of the questions in these exercises, as well as gaining a better understanding of the pair of linear equations in two variables.

• We can gain practise by solving all of the questions based on graphical representations of linear equations in two variables in the NCERT solution for Class 10th Maths chapter 3 exercise 3.1 and get a general idea about the topic, and we can get more marks in the examination if we practise it thoroughly.

• Exercise 3.1 Class 10 Maths, in grasping the fundamental notion of graphical and algebraic representations of linear equations in two variables, as well as the many types of solutions and their graphs, which are key concepts in the chapter.

Also see-

NCERT Solutions of Class 10 Subject Wise

Subject Wise NCERT Exemplar Solutions

Frequently Asked Questions (FAQs)

Q: What are the coefficients of the equation 7x - 5y = 10 ?
A:

The concepts related to coefficients of the equations are discussed in ex 3.1 class 10 comprehensively. Students can practice these questions and answer. as per this question, the coefficient of x is 7 and the coefficient of y is -5.

Q: What is the constant of the equation 7x - 5y = 10 ?
A:

The concepts related to coefficients of the equations are discussed in class 10 maths ex 3.1 comprehensively. Students can practice these questions and answer. As per this question, the constant of the equation 7x - 5y = 10 is 10.

Q: How many solutions are there for linear equations in two variables if the equations are consistent and dependent ?
A:

Concepts related to consistent and dependent equations are discussed in 10th class maths exercise 3.1 answers . according to this concept If the equations are consistent and dependent, then linear equations in two variables have infinite number solutions.

Q: How many methods are there in solving the linear equations in two variables?
A:

Mathematically, there are five methods in solving the linear equations in two variables. Practice problems enumerated in class 10 maths ex 3.1 to get deeper understanding of these methods.

Q: Find the value of y in 5x - y = 10 if x = 1 .
A:

Putting x = 1 in 5x - y = 10 

5(1) - y = 10 

-y = 10 - 5

Thus y = -5

Q: Solve 4x-10=2x-4
A:

On interchanging their sides, 

4x - 2x = 10 - 4

2x = 6

Thus x = 3 

Q: What is the substitution method according to NCERT solutions for Class 10 Maths chapter 3 exercise 3.1 ?
A:

Substituting the value of one variable in the other equation to get the value of another variable is known as the substitution method. Practice problems discussed in class 10 ex 3.1 to get deeper understanding about the substitution method to get solution of an equation. 

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english paper class 11 haf yearly 2025-26

Hi! If you’re looking for the Class 11 English half yearly question paper for 2025-26 (CBSE board), you’ll find the right resource once you check the link provided from Careers360. Solving previous or sample papers is a smart way to prepare, as it helps you understand the question types, marking scheme, and important topics. This practice will boost your confidence and help you manage your time well in the actual exam.
https://school.careers360.com/boards/cbse/cbse-class-11-half-yearly-sample-papers-2025-26

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C
Chelsie G
17 Nov'25
10 class 2024 2025 advarshik paper english

Hi dear candidate,

Could you please specify us the board of education for which you need the half yearly question papers of class X so that we can help you further.

Below are few links which may help you and it has all the subjects with English as well:

CBSE Class 10 Half Yearly Exam Question Paper 2025-26 with Answer Key & Analysis

ICSE Class 10 Half Yearly Sample Papers 2025-26 PDF (All Subjects)

BEST REGARDS

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A
Aryan
18 Nov'25
class 10 state syllabus english medium year 2025 2026 send blue print

Hi dear candidate,

Can you please specify the board of education or state for which you need to know the exam pattern and syllabus so that we can guide you accordingly.

Since, most of the boards uses NCERT as base syllabus, you can refer to the link below:

NCERT Syllabus for Class 10 – All Subjects PDF Download 2025-26

Exam pattern:

CBSE 10th New Exam Pattern 2026- Marking Scheme, Subject-Wise Exam Pattern

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18 Nov'25
I want information of class 10 2026 board exam

The CBSE Class 10th Board Exams for the 2026 session will follow the revised curriculum, emphasizing competency-based questions.

  • Conducting Body: Central Board of Secondary Education (CBSE).

  • Exam Period: The main theory exams are typically held between February and April 2026.

  • Grading: Based on marks in five main subjects plus internal assessment marks (often 20 marks per subject) provided by the school.

  • Passing Criteria: You must achieve at least 33% overall in each subject (theory + practical/internal assessment combined) to be declared pass.

Key Preparation Strategy

The most crucial element of your preparation is understanding the exam structure:

  • Syllabus: Strictly adhere to the rationalized syllabus released by CBSE for the 2025-26 academic year.

  • Practice: Your primary resource should be the latest sample papers and previous year question papers. These accurately reflect the format and types of competency questions being asked.

For the most comprehensive and official announcements, including the detailed time table and access to crucial practice materials, always check the official board updates, as tracked by Careers360: https://school.careers360.com/exams/cbse-class-10th .

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17 Nov'25
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HELLO,

If you want admission to 9th grade under the CBSE board in Andhra Pradesh , visit nearby CBSE affiliated schools during the admission period that is generally from January  to April or you can check the official websites of the schools in which you are interested for admission if they are accepting the admissions now .

After deciding the school and getting information about admission deadline from the school you can fill out the admission form with documents submission like your previous report card , transfer certificate and birth certificate , they make take entrance test or interview to confirm your admission

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