Careers360 Logo
NCERT Solutions for Exercise 3.6 Class 10 Maths Chapter 3 - Pair of Linear Equations in two variables

NCERT Solutions for Exercise 3.6 Class 10 Maths Chapter 3 - Pair of Linear Equations in two variables

Edited By Ramraj Saini | Updated on Nov 13, 2023 03:23 PM IST | #CBSE Class 10th

NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.6

NCERT Solutions for class 10 maths ex 3.6 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 3.6 class 10 consists of two questions, each with subparts. The first is straightforward, requiring only direct substitutions of the mathematical formula, whereas the second involves word problems. In this exercise, the majority of the variables are in fractional form, meaning that they are nonlinear, since the variables are now infraction, we can’t take the value of the denominator as zero because it will be against the definition of the fraction.

This Story also Contains
  1. NCERT Solutions For Class 10 Maths Chapter 3 Exercise 3.6
  2. Download Free Pdf of NCERT Solutions for Class 10 Maths chapter 3 exercise 3.6
  3. Assess NCERT Solutions for Class 10 Maths chapter 3 exercise 3.6
  4. More About Ncert Solutions For Class 10 Maths Exercise 3.6
  5. Benefits of NCERT Solutions for Class 10 Maths Exercise 3.6
  6. NCERT Solutions of Class 10 Subject Wise
  7. Subject Wise NCERT Exemplar Solutions
NCERT Solutions for Exercise 3.6 Class 10 Maths Chapter 3 - Pair of Linear Equations in two variables
NCERT Solutions for Exercise 3.6 Class 10 Maths Chapter 3 - Pair of Linear Equations in two variables

These class 10 maths ex 3.6 solutions are designed as per the students demand covering comprehensive, step by step solutions of every problem. 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

JEE Main Important Mathematics Formulas

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

Download Free Pdf of NCERT Solutions for Class 10 Maths chapter 3 exercise 3.6

Download PDF

Assess NCERT Solutions for Class 10 Maths chapter 3 exercise 3.6

Pair of Linear Equations in Two Variables Class 10 Chapter 3 Excercise: 3.6

Q1(i) Solve the following pairs of equations by reducing them to a pair of linear equations:

12x+13y=213x+12y=136

Answer:

Given Equations,

12x+13y=213x+12y=136

Let,

1x=pand1y=q

Now, our equation becomes

p2+q3=2

3p+2q=12........(1)

And

p3+q2=136

2p+3q=13..........(2)

By Cross Multiplication method,

pb1c2b2c1=qc1a2c2a1=1a1b2a2b1

p(2)(13)(3)(12)=q(12)(2)(13)(3)=1(3)(3)(2)(2)

p26+36=q24+39=194

p10=q15=15

p=2,andq=3

And Hence,

x=12andy=13.

Q1(ii) Solve the following pairs of equations by reducing them to a pair of linear equations:

2x+3y=24x9y=1

Answer:

Given Equations,

2x+3y=24x9y=1

Let,

1x=pand1y=q

Now, our equation becomes

2p+3q=2........(1)

And

4p9q=1..........(2)

By Cross Multiplication method,

pb1c2b2c1=qc1a2c2a1=1a1b2a2b1

p(3)(1)(9)(2)=q(2)(4)(1)(2)=1(2)(9)(4)(3)

p318=q82=11812

p15=q10=130

p=12,andq=13

So,

p=12=1xx=4

q=13=1yy=9 .

And hence

x=4andy=9.

Q1(iii) Solve the following pairs of equations by reducing them to a pair of linear equations:

4x+3y=143x4y=23

Answer:

Given Equations,

4x+3y=143x4y=23

Let,

1x=pandy=q

Now, our equation becomes

4p+3q=14........(1)

And

3p4q=23..........(2)

By Cross Multiplication method,

pb1c2b2c1=qc1a2c2a1=1a1b2a2b1

p(3)(23)(4)(14)=q(14)(3)(23)(4)=1(4)(4)(3)(3)

p6956=q42+92=1169

p125=q50=125

p=5,andq=2

And Hence,

x=15andy=2.

Q1(iv) Solve the following pairs of equations by reducing them to a pair of linear equations:

5x1+1y2=26x13y2=1

Answer:

Given Equations,

5x1+1y2=26x13y2=1

Let,

1x1=pand1y2=q

Now, our equation becomes

5p+q=2........(1)

And

6p3q=1..........(2)

Multiplying (1) by 3 we get

15p+3q=6..........(3)

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

21p=7

p=13

Putting this in (2)

6(13)3q=1

3q=1

q=13

Now,

p=13=1x1x1=3x=4

q=13=1y2y2=3x=5

Hence,

x=4,andy=5.

Q1(v) Solve the following pairs of equations by reducing them to a pair of linear equations:

7x2yxy=58x+7yxy=15

Answer:

Given Equations,

7x2yxy=57y2x=58x+7yxy=158y+7x=15

Let,

1x=pand1y=q

Now, our equation becomes

7q2p=5........(1)

And

8q+7p=15..........(2)

By Cross Multiplication method,

qb1c2b2c1=pc1a2c2a1=1a1b2a2b1

q(2)(15)(7)(5)=p(5)(8)(15)(7)=1(7)(7)(8)(2)

q30+35=p40+105=149+16

q65=p65=165

p=1,andq=1

And Hence,

x=1andy=1.

Q1(vi) Solve the following pairs of equations by reducing them to a pair of linear equations:

6x+3y=6xy2x+4y=5xy

Answer:

Given Equations,

6x+3y=6xy6xxy+3yxy=66y+3x=6and 2x+4y=5xy2xxy+4yxy=52y+4x=5

Let,

1x=pand1y=q

Now, our equation becomes

6q+3p=6........(1)

And

2q+4p=5..........(2)

By Cross Multiplication method,

qb1c2b2c1=pc1a2c2a1=1a1b2a2b1

q(3)(5)(6)(4)=p(6)(2)(6)(5)=1(6)(4)(3)(2)

q15+24=p12+30=1246

q9=p18=118

q=12andp=1

And Hence,

x=1andy=2.

Q1(vii) Solve the following pairs of equations by reducing them to a pair of linear equations:
10x+y+2xy=415x+y5xy=2


Answer:

Given Equations,

10x+y+2xy=415x+y5xy=2

Let,

1x+y=pand1xy=q

Now, our equation becomes

10p+2q=4........(1)

And

15p5q=2..........(2)

By Cross Multiplication method,

pb1c2b2c1=qc1a2c2a1=1a1b2a2b1

p(2)(2)(5)(4)=q(4)(15)(2)(10)=1(10)(5)(15)(2)

p420=q6020=15030

p16=q80=180

p=15,andq=1

Now,

p=15=1x+y

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

And,

q=1=1xy

xy=1...........(4)

Adding (3) and (4) we get,

2x=6

x=3

Putting this value in (3) we get,

3+y=5

y=2

And Hence,

x=3andy=2.

Q1(viii) Solve the following pairs of equations by reducing them to a pair of linear equations:

13x+y+13xy=3412(3x+y)12(3xy)=18


Answer:

Given Equations,

13x+y+13xy=3412(3x+y)12(3xy)=18

Let,

13x+y=pand13xy=q

Now, our equation becomes

p+q=34.........(1)

And

p2q2=18pq=14..........(2)

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

2p=3414

2p=24

p=14

Putting this value in (1)

14+q=34

q=3414

q=24

q=12

Now,

p=14=13x+y

3x+y=4...........(3)

And

q=12=13xy

3xy=2............(4)

Now, Adding (3) and (4), we get

6x=4+2

6x=6

x=1

Putting this value in (3),

3(1)+y=4

y=43

y=1

Hence,

x=1,andy=1

Q2(i) Formulate the following problems as a pair of equations and hence find their solutions: Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current.

Answer:

Let the speed of Ritu in still water be x and speed of current be y,

Let's solve this problem by using relative motion concept,

the relative speed when they are going in the same direction (downstream)= x +y

the relative speed when they are going in the opposite direction (upstream)= x - y

Now, As we know,

Relative distance = Relative speed * time .

So, According to the question,

x+y=202

x+y=10.........(1)

And,

xy=42

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

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

2x=10+2

2x=12

x=6

Putting this in (2)

6y=2

y=62

y=4

Hence,

x=6andy=4.

Hence Speed of Ritu in still water is 6 km/hour and the speed of the current is 4 km/hour

Q2(ii) Formulate the following problems as a pair of equations and hence find their solutions: 2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.

Answer:

Let the number of days taken by woman and man be x and y respectively,

The proportion of Work done by a woman in a single day

=1x

The proportion of Work done by a man in a single day

=1y

Now, According to the question,

4(2x+5y)=1

(2x+5y)=14

Also,

3(3x+6y)=1

(3x+6y)=13

Let,

1x=pand1y=q

Now, our equation becomes

2p+5q=14

8p+20q=1........(1)

And

3p+6p=13

9p+18p=1.............(2)

By Cross Multiplication method,

pb1c2b2c1=qc1a2c2a1=1a1b2a2b1

p(20)(1)(18)(1)=q(1)(9)(8)(1)=1(8)(18)(20)(9)

p20+18=q9+8=114660

p2=q1=136

p=118,andq=136

So,

x=18andy=36.

Q2(iii) Formulate the following problems as a pair of equations and hence find their solutions: Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.

Answer:

Let the speed of the train and bus be u and v respectively

Now According to the question,

60u+240v=4

And

100u+200v=4+16

100u+200v=256

Let,

1u=pand1v=q

Now, our equation becomes

60p+140q=4

15p+60q=1.........(1)

And

100p+200q=256

4p+8q=16

24p+48q=1..........(2)

By Cross Multiplication method,

pb1c2b2c1=qc1a2c2a1=1a1b2a2b1

q(60)(1)(48)(1)=p(1)(24)(1)(15)=1(15)(48)(60)(24)

p60+48=q24+15=17201440

p12=q9=1720

p=12720=160,andq=9720=180

And Hence,

x=60andy=80

Hence the speed of the train and bus are 60 km/hour and 80 km/hour respectively.

More About Ncert Solutions For Class 10 Maths Exercise 3.6

NCERT solutions for Class 10 Maths exercise 3.6- consists of two extremely important questions. In order to answer the first question, you must reduce the pair of equations to a pair of linear equations. Students must express problems as a pair of equations in order to determine their answers to the second question. Furthermore, exercise 3.6 is a more advanced chapter exercise. Above all, this task is an excellent technique to assess a student's ability to solve linear equations in two variables. 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 3.6

  • NCERT book Exercise 3.6 Class 10 Maths, is based on the basic idea of solving a pair of equations with fractional variables.
  • NCERT solutions for Class 10 Maths chapter 3 exercise 3.6 helps to solve complex non-linear equations by simplifying it to simple linear equations.
  • If you go through the NCERT solution for Class 10 Maths chapter 3 exercise 3.6, we can see that we will have to use the previous solving methods like substitution and elimination. Thus, this part helps us to clear our previous concepts too.
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

Also see-

NCERT Solutions of Class 10 Subject Wise

Subject Wise NCERT Exemplar Solutions

Frequently Asked Questions (FAQs)

1. What are the methods used for solving linear equation in two variables?

We use substitution method, graphical and elimination method etc.

2. Which one of the methods is easier compared to the other between Graphical and Elimination Method?

Because it is time-efficient and does not take a long time to complete. Hence, the elimination method is preferred.

3. What is the basic concept behind NCERT solutions for Class 10 Maths 3 exercise 3.4?

In this exercise, the majority of the variables are in fractional form, meaning that they are nonlinear, since the variables are now infractions, we can’t take the value of the denominator as zero because it will be against the definition of the fraction.

4. How do we solve the majority of the variables which are in fractional form?

We substitute the fraction variable as another new variable; thus, we get two new linear equations that we can solve easily.

5. Is there a role for substitution in the elimination method?

Yes, we can get the value of the second equation by substituting the value of the first variable into any of the equations.

6. Do we need any kind of substitution in order to get the final answer?

Yes, we need substitution in order to get the final answer.

Articles

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 Nottingham, Nottingham
 University Park, Nottingham NG7 2RD

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

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

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.

View All

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

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

 

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

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

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 .

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

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.

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.

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

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

Back to top