Careers360 Logo
School
Search Colleges, Exams, Schools & more
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

Edited By Ramraj Saini | Updated on Nov 08, 2023 07:42 PM IST | #CBSE Class 10th

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.

This Story also Contains
  1. NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.1
  2. Download PDF of NCERT Solutions For Class 10 Maths Chapter 1 Exercise 3.1
  3. Access Exercise 3.1 Class 10 Maths Answers
  4. More About NCERT Solutions for Class 10 Maths Exercise 3.1
  5. Benefits of NCERT Solutions for Class 10 Maths Exercise 3.1
  6. NCERT Solutions of Class 10 Subject Wise
  7. Subject Wise NCERT Exemplar Solutions
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

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.

NEET/JEE Coaching Scholarship

Get up to 90% Scholarship on Offline NEET/JEE coaching from top Institutes

Apply
JEE Main Important Mathematics Formulas

As per latest 2024 syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters

Get now

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

Download PDF

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×(y−7)

⇒x−7=7y−49

⇒x−7y=−42.....(1)

Also,

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

⇒x+3=3y+9

⇒x−3y=6.....(2)

Now, let's represent both equations graphically,

From (1), we get

y=x+427

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=x−63

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=3900−3x6

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=1300−x3

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=300−4x2=150−2x

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

X
50
60
70
Y
50
30
10

Graph:

graph

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-

NEET/JEE Offline Coaching
Get up to 90% Scholarship on your NEET/JEE preparation from India’s Leading Coaching Institutes like Aakash, ALLEN, Sri Chaitanya & Others.
Apply Now

NCERT Solutions of Class 10 Subject Wise

Subject Wise NCERT Exemplar Solutions

Frequently Asked Questions (FAQs)

1. What are the coefficients of the equation 7x - 5y = 10 ?

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.

2. What is the constant of the equation 7x - 5y = 10 ?

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.

3. How many solutions are there for linear equations in two variables if the equations are consistent and dependent ?

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.

4. How many methods are there in solving the linear equations in two variables?

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.

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

Putting x = 1 in 5x - y = 10 

5(1) - y = 10 

-y = 10 - 5

Thus y = -5

6. Solve 4x-10=2x-4

On interchanging their sides, 

4x - 2x = 10 - 4

2x = 6

Thus x = 3 

7. What is the substitution method according to NCERT solutions for Class 10 Maths chapter 3 exercise 3.1 ?

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. 

Also Read

Articles

Upcoming School Exams

Central Board of Secondary Education Class 12th Examination

Admit Card Date:03 February,2025 - 04 April,2025

Telangana State Secondary School Certificate Examination

Admit Card Date:07 March,2025 - 04 April,2025

Karnataka Secondary School Leaving Certificate Examination

Admit Card Date:10 March,2025 - 05 April,2025

Telangana Residential Junior Colleges Common Entrance Test

Application Date:24 March,2025 - 23 April,2025

Chattisgarh State Open School 10th Examination

Admit Card Date:25 March,2025 - 17 April,2025

View All School Exams

Certifications By Top Providers

Edx
 1115 courses
Coursera
 816 courses
Udemy
 394 courses
Futurelearn
 295 courses
Harvard University, Cambridge
 98 courses
University of Michigan, Ann Arbor
 83 courses

Explore Top Universities Across Globe

University of Essex, Colchester
  Wivenhoe Park Colchester CO4 3SQ
University College London, London
  Gower Street, London, WC1E 6BT
The University of Edinburgh, Edinburgh
  Old College, South Bridge, Edinburgh, Post Code EH8 9YL
University of Bristol, Bristol
  Beacon House, Queens Road, Bristol, BS8 1QU
University of Delaware, Newark
  Newark, DE 19716
University of Nottingham, Nottingham
  University Park, Nottingham NG7 2RD

Related E-books & Sample Papers

Questions related to CBSE Class 10th

Have a question related to CBSE Class 10th ?
i studied 1 to 10th CBSE board abroad and 11th 12th in karnataka state board . i am a domicile of karnataka and comes under minority, income under 5 lakhs. how neet councillng will allocate my seat

Hello

Since you are a domicile of Karnataka and have studied under the Karnataka State Board for 11th and 12th , you are eligible for Karnataka State Quota for admission to various colleges in the state.

1. KCET (Karnataka Common Entrance Test): You must appear for the KCET exam, which is required for admission to undergraduate professional courses like engineering, medical, and other streams. Your exam score and rank will determine your eligibility for counseling.

2. Minority Income under 5 Lakh : If you are from a minority community and your family's income is below 5 lakh, you may be eligible for fee concessions or other benefits depending on the specific institution. Some colleges offer reservations or other advantages for students in this category.

3. Counseling and Seat Allocation:

After the KCET exam, you will need to participate in online counseling.

You need to select your preferred colleges and courses.

Seat allocation will be based on your rank , the availability of seats in your chosen colleges and your preferences.

4. Required Documents :

Domicile Certificate (proof that you are a resident of Karnataka).

Income Certificate (for minority category benefits).

Marksheets (11th and 12th from the Karnataka State Board).

KCET Admit Card and Scorecard.

This process will allow you to secure a seat based on your KCET performance and your category .

check link for more details

https://medicine.careers360.com/neet-college-predictor

Hope this helps you .

Read Complete Answer
Mitali Sharma 30 January,2025
show the previous year exams ?

Hello Aspirant,  Hope your doing great,  your question was incomplete and regarding  what exam your asking.

Read Complete Answer
SWETCHCHA MISKA 10 July,2024
as an icse student in class 10 is above 80 percent good enough to get into commerce in 11th cbse

Yes, scoring above 80% in ICSE Class 10 exams typically meets the requirements to get into the Commerce stream in Class 11th under the CBSE board . Admission criteria can vary between schools, so it is advisable to check the specific requirements of the intended CBSE school. Generally, a good academic record with a score above 80% in ICSE 10th result is considered strong for such transitions.

Read Complete Answer
Manasvini Gupta 23 July,2024
i had cleared 10th from cbse in 2022 2 years ago now i wish to apply for 12th as private candidate in 2025. can i do so?

hello Zaid,

Yes, you can apply for 12th grade as a private candidate .You will need to follow the registration process and fulfill the eligibility criteria set by CBSE for private candidates.If you haven't given the 11th grade exam ,you would be able to appear for the 12th exam directly without having passed 11th grade. you will need to give certain tests in the school you are getting addmission to prove your eligibilty.

best of luck!

Read Complete Answer
Ashvadha 03 July,2024
i had cleared 10th in 2022 from cbse can i apply for 12th as private candidate this year?

According to cbse norms candidates who have completed class 10th, class 11th, have a gap year or have failed class 12th can appear for admission in 12th class.for admission in cbse board you need to clear your 11th class first and you must have studied from CBSE board or any other recognized and equivalent board/school.

You are not eligible for cbse board but you can still do 12th from nios which allow candidates to take admission in 12th class as a private student without completing 11th.

Read Complete Answer
sadafreen356 03 July,2024
View All

Popular CBSE Class 10th Questions

A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1)

0.34\; J

 Option 2)

0.16\; J
Option 3)

1.00\; J

 Option 4)

0.67\; J
Read More

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

Option 1)

2.45×10−3 kg

 Option 2)

 6.45×10−3 kg
Option 3)

 9.89×10−3 kg

 Option 4)

12.89×10−3 kg

 
Read More

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1)

2,000 \; J - 5,000\; J

 Option 2)

200 \, \, J - 500 \, \, J
Option 3)

2\times 10^{5}J-3\times 10^{5}J

 Option 4)

20,000 \, \, J - 50,000 \, \, J
Read More

A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

Option 1)

K/2\,

 Option 2)

\; K\;
Option 3)

zero\;

 Option 4)

K/4
Read More

In the reaction,

2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

Option 1)

11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

 Option 2)

6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced
Option 3)

33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

 Option 4)

67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .
Read More

How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

Option 1)

0.02

 Option 2)

3.125 × 10-2
Option 3)

1.25 × 10-2

 Option 4)

2.5 × 10-2
Read More

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1)

decrease twice

 Option 2)

increase two fold
Option 3)

remain unchanged

 Option 4)

be a function of the molecular mass of the substance.
Read More

With increase of temperature, which of these changes?

Option 1)

Molality

 Option 2)

Weight fraction of solute
Option 3)

Fraction of solute present in water

 Option 4)

Mole fraction.
Read More

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

Option 1)

twice that in 60 g carbon

 Option 2)

6.023 × 1022
Option 3)

half that in 8 g He

 Option 4)

558.5 × 6.023 × 1023
Read More

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

Option 1)

less than 3

 Option 2)

more than 3 but less than 6
Option 3)

more than 6 but less than 9

 Option 4)

more than 9
Read More

Colleges After 12th

Study Resources, Applications and Opportunities

NEET/JEE Coaching Scholarship
NEET/JEE Coaching Scholarship
Apply

Get up to 90% Scholarship on Offline NEET/JEE coaching from top Institutes

NEET Most scoring concepts
NEET Most scoring concepts
Get now

This ebook serves as a valuable study guide for NEET 2025 exam.

NEET Previous 10 Year Questions
NEET Previous 10 Year Questions
Get now

This e-book offers NEET PYQ and serves as an indispensable NEET study material.

JEE Main Important Physics formulas
JEE Main Important Physics formulas
Get now

As per latest 2024 syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters

JEE Main Important Chemistry formulas
Get now

As per latest 2024 syllabus. Chemistry formulas, equations, & laws of class 11 & 12th chapters

TOEFL ® Registrations 2024
Apply

Accepted by more than 11,000 universities in over 150 countries worldwide

View All Application Forms
News and Notifications
CBSE 10th Result 2025: Evaluation criteria, marking scheme, supplementary exams; what we know
March 31, 2025 - 03:51 PM IST
Holding CBSE Class 10 twice can lead to ‘paper leaks, irregularities’, warns parliament panel
March 27, 2025 - 11:00 AM IST
When will CBSE Class 10 results 2025 be declared? Overall exam paper analysis
March 22, 2025 - 03:58 PM IST
CBSE will rope in external agency for skill, vocational subject exams
March 22, 2025 - 12:23 PM IST
CBSE adopts new re-evaluation process, split Class 10 science question papers; will test on-screen marking
March 21, 2025 - 06:10 PM IST
CBSE Board Exam 2025 Live: Class 10 CS, IT, AI paper 'easy, straightforward'; difficulty level, answer key
March 18, 2025 - 09:58 PM IST
CBSE Class 10 CS, IT AI Exam Analysis 2025: Paper 'easy, well-balanced'; section-wise difficulty level
March 18, 2025 - 03:04 PM IST

Stay up-to date with CBSE Class 10th News

Back to top