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NCERT Solutions for Exercise 3.4 Class 10 Maths Chapter 3 - Pair of Linear Equations in two variables

NCERT Solutions for Exercise 3.4 Class 10 Maths Chapter 3 - Pair of Linear Equations in two variables

Edited By Komal Miglani | Updated on Apr 29, 2025 04:52 PM IST | #CBSE Class 10th

There are various methods for solving the linear equation. In the previous exercises graphical method and one of the algebraic methods for solving the equation have been discussed. There are many algebraic methods for solving equations, like substitution and elimination methods. Similar to the substitution method elimination method is also used to solve the linear equation. In this method, multiply the equation by numbers to make the coefficient of the equation equal. This will help to eliminate the value and get the solution.

This Story also Contains
  1. Download Free PDF of NCERT Solutions for Class 10 Maths Chapter 3 Exercise 3.3
  2. Assess NCERT Solutions for Class 10 Maths Chapter 3 Exercise 3.3
  3. Topics Covered in Chapter 3 Pair of Linear Equations in Two Variables: Exercise 3.3
  4. NCERT Solutions of Class 10 Subject Wise
  5. NCERT Exemplar Solutions of Class 10 Subject Wise
NCERT Solutions for Exercise 3.4 Class 10 Maths Chapter 3 - Pair of Linear Equations in two variables
NCERT Solutions for Exercise 3.4 Class 10 Maths Chapter 3 - Pair of Linear Equations in two variables

These class 10 maths exercise 3.3 solutions are designed as per the students' demand, covering comprehensive, step-by-step solutions of every problem. Practice is necessary for all these questions to command the concepts, boost confidence and in-depth understanding of concepts. In the exercise, all the NCERT solutions are covered according to the syllabus of the NCERT. These solutions help the students to understand the concept in depth. This exercise included all the questions given in the NCERT Books. In exercise 3.3 of the NCERT, the chapter solutions are explained in detail.

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Download Free PDF of NCERT Solutions for Class 10 Maths Chapter 3 Exercise 3.3

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Assess NCERT Solutions for Class 10 Maths Chapter 3 Exercise 3.3

Q1(i) Solve the following pair of linear equations by the elimination method and the substitution method :

x+y=5 and 2x3y=4

Answer:

Elimination Method:

Given, equations

x+y=5............(1) and 2x3y=4........(2)

Now, multiplying (1) by 3 we get

3x+3y=15............(3)

Now, adding (2) and (3), we get

2x3y+3x+3y=4+15

5x=19

x=195

Substituting this value in (1), we get

195+y=5

y=5195

y=65

Hence,

x=195andy=65

Substitution method :

Given, equations

x+y=5............(1) and 2x3y=4........(2)

Now, from (1) we have,

y=5x.......(3)

Substituting this value in (2)

2x3(5x)=4

2x15+3x=4

5x=19

x=195

Substituting this value of x in (3)

y=5x=5195=65

Hence,

x=195andy=65

Q1(ii) Solve the following pair of linear equations by the elimination method and the substitution method :

3x+4y=10 and 2x2y=2

Answer:

Elimination Method:

Given, equations

3x+4y=10............(1) and 2x2y=2..............(2)

Now, multiplying (2) by 2 we get

4x4y=4............(3)

Now, adding (1) and (3), we get

3x+4y+4x4y=10+4

7x=14

x=2

Putting this value in (2) we get

2(2)2y=2

2y=2

y=1

Hence,

x=2andy=1

Substitution method :

Given, equations

3x+4y=10............(1) and 2x2y=2..............(2)

Now, from (2) we have,

y=2x22=x1.......(3)

Substituting this value in (1)

3x+4(x1)=10

3x+4x4=10

7x=14

x=2

Substituting this value of x in (3)

y=x1=21=1

Hence, x=2andy=1

Q1(iii} Solve the following pair of linear equations by the elimination method and the substitution method: (iii) 3x5y4=0 and 9x=2y+7

Answer:

Elimination Method:

Given, equations

3x5y4=0..........(1) and 9x=2y+7

9x2y7=0........(2)

Now, multiplying (1) by 3 we get

9x15y12=0............(3)

Now, subtracting (3) from (2), we get

9x2y79x+15y+12=0

13y+5=0

y=513

Putting this value in (1), we get

3x5(513)4=0

3x=42513

3x=2713

x=913

Hence,

x=913andy=513

Substitution method :

Given, equations

3x5y4=0..........(1) and 9x=2y+7

9x2y7=0........(2)

Now, from (2) we have,

y=9x72.......(3)

Substituting this value in (1)

3x5(9x72)4=0

6x45x+358=0

39x+27=0

x=2739=913

Substituting this value of x in (3)

y=9(9/13)72=81/1372=513

Hence, x=913andy=513

Q1(iv) Solve the following pair of linear equations by the elimination method and the substitution method :(iv) x2+2y3=1 and xy3=3

Answer:

Elimination Method:

Given, equations

x2+2y3=1........(1) and xy3=3............(2)

Now, multiplying (2) by 2, we get

2x2y3=6............(3)

Now, adding (1) and (3), we get

x2+2y3+2x2y3=1+6

5x2=5

x=2

Putting this value in (2), we get

2y3=3

y3=1

y=3

Hence,

x=2andy=3

Substitution method :

Given, equations

x2+2y3=1........(1) and xy3=3............(2)

Now, from (2) we have,

y=3(x3)......(3)

Substituting this value in (1)

x2+2(3(x3))3=1

x2+2x6=1

5x2=5

x=2

Substituting this value of x in (3)

y=3(x3)=3(21)=3

Hence, x=2andy=3

Q2(i) Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method : (i) If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes 12 if we only add 1 to the denominator. What is the fraction?

Answer:

Let the numerator of the fraction be x, and the denominator is y,

Now, according to the question,

x+1y1=1

x+1=y1

xy=2.........(1)

Also,

xy+1=12

2x=y+1

2xy=1..........(2)

Now, subtracting (1) from (2), we get

x=3

Putting this value in (1)

3y=2

y=5

Hence, x=3andy=5

And the fraction is: 35

Q2(ii) Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method : (ii) Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?

Answer:

Let the age of Nuri be x and the age of Sonu be y.

Now, according to the question

x5=3(y5)

x5=3y15

x3y=10.........(1)

Also,

x+10=2(y+10)

x+10=2y+20

x2y=10........(2)

Now, subtracting (1) from (2), we get

y=20

Putting this value in (2)

x2(20)=10

x=50

Hence, the age of Nuri is 50 and the age of Nuri is 20.

Q2(iii) Form the pair of linear equations in the following problems and find their solutions (if they exist) by the elimination method : (iii) The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

Answer:

Let the unit digit of the number be x and the 10's digit be y.

Now, according to the question,

x+y=9.......(1)

Also

9(10y+x)=2(10x+y)

90y+9x=20x+2y

88y11x=0

8yx=0.........(2)

Now adding (1) and (2), we get,

9y=9

y=1

Now putting this value in (1)

x+1=9

x=8

Hence, the number is 18.

Q2(iv) Form the pair of linear equations in the following problems and find their solutions (if they exist) by the elimination method : (iv) Meena went to a bank to withdraw Rs 2000. She asked the cashier to give her Rs 50 and Rs 100 notes only. Meena got 25 notes in all. Find how many notes of Rs 50 and Rs 100 she received.

Answer:

Let the number of Rs 50 notes be x and the number of Rs 100 notes be y.

Now, according to the question,

x+y=25..........(1)

And

50x+100y=2000

x+2y=40.............(2)

Now, subtracting (1) from (2), we get

y=15

Putting this value in (1).

x+15=25

x=10

Hence, Meena received 10, 50 Rs notes and 15, 100 Rs notes.

Topics Covered in Chapter 3 Pair of Linear Equations in Two Variables: Exercise 3.3

  1. Elimination Method: In this method, multiply the equations if required to make the coefficient of the equation equal. Then, eliminate one of the variables by adding or subtracting the equations.
  2. Reducing Equations to a Linear Form: In some problems need to simplify the equation, or in some equations need to apply the substitution method to convert the equation into a standard linear equation. After reducing these equations, the elimination method is applied.
  3. Solving Word Problems: In this exercise, some questions are based on word problems. To solve these questions, these word problems are converted into a pair of linear equations for solving them.
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NCERT Solutions of Class 10 Subject Wise

Students must check the NCERT solutions for class 10 of the Mathematics and Science Subjects.

JEE Main Important Mathematics Formulas

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

NCERT Exemplar Solutions of Class 10 Subject Wise

Students must check the NCERT Exemplar solutions for class 10 of the Mathematics and Science Subjects.

Frequently Asked Questions (FAQs)

1. Choose the convenient and time efficient method to solve linear a pair of linear equations?
  1. Graphical Method 

  2. Elimination method 

Elimination method as it is time-efficient and not lengthy.

2. What is the basic concept of elimination method according to NCERT solutions for Class 10 Maths 3 exercise 3.3?

We multiply both the equations with some non-zero constant to eliminate one of the variables by adding both of the new equations.

3. Why do we multiply both the equations with some non-zero variable?

In order to make the coefficient of one of the variables numerically equal but with opposite signs so that they get cancelled when we add them together.

4. Does substitution play any role in elimination method?

Yes, once we find the value of the first variable, we substitute its value in any of the equation to get the value of the second equation.

5. Why graphical method is not always useful?

It doesn’t provide us the desired point if the values are irrational.

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Questions related to CBSE Class 10th

Have a question related to CBSE Class 10th ?

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

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Hope this helps you .

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

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.

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!

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.

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