NCERT Solutions for Class 10 Maths Exercise 3.4 of Chapter 3 Linear Equation in Two Variables - Future Study Point

# NCERT Solutions for Class 10 Maths Exercise 3.4 of Chapter 3 Linear Equation in Two Variables

NCERT Solutions for Class 10 Maths Exercise 3.4 of Chapter 3Pair of Linear Equations in Two Variables are created here for boosting your preparation of the CBSE Board exam.NCERT Solutions for Class 10 Maths Exercise 3.4 of Chapter 3 Pair of Linear Equations in Two Variables are solved by a step-by-step method by an expert of CBSE maths. NCERT solutions are the most important study material to clear your basic concept of maths. Here you can study all study notes related to CBSE science and maths.

## NCERT Solutions for Class 10 Maths Exercise 3.4 of Chapter 3 Linear Equation in Two Variables

Q1. Solve the following pair of linear equations by the elimination method and the substitution method:

(i) x +y = 5 and 2x -3y = 4

(ii) 3x + 4y =10 and 2x -2y = 2

(iii) 3x -5y -4 = 0 and 9x =2y +7

(iv) x/2  +2y/3 = -1 and x – y/3 = 3

Ans.The given pair of linear  equations is

x +y=5 ……(i)

2x -3y = 4…(ii)

Multiplying the equation (i) by 2,we get equation (iii)

2x +2y=10….(iii)

Substracting equation (iii) from equation (ii)

-5y = -6

y = 6/5

Putting the value y = 6/5 in equation (i)

x + 6/5 = 5

x = 5 – 6/5 =(25 – 6)/5 = 19/5

Hence value of x is 6/5 and value of y is 19/5

(ii) The given equations are

3x + 4y =10…..(i) and 2x -2y = 2…..(ii)

Multiplying equation (i) by 2 and equation (ii) by 3,we get the equation (iii) and equation (iv)

6x + 8y =20…..(iii) and 6x -6y =6….(iv)

Substracting equation (iv) from equation (iii),we get

14y = 14

y = 1

Putting the value of y in equation (i)

3x +4×1=10

3x + 4 =10

3x = 6

x = 2

Hence the value of x is 2 and value of y is 1

(iii) The given equations are

3x -5y -4 = 0 (i) and 9x =2y +7(i.e 9x -2y -7=0)…..(ii)

Multiplying equation (i) by 3,we get equation (iii)

9x -15y -12 = 0 (iii)

Substracting equation (iii) from equation (ii)

13y+5 =0

y = -5/13

Putting this value of y in equation (i)

3x -5(-5/13) -4 = 0

3x +25/13 = 4

3x = 4 -(25/13)

3x = (52-25)/13 = 27/13

x = 9/13

Hence the value of x is 9/13 and value of y is -5/13

(iv) The given equations are x/2  +2y/3 = -1 and x – y/3 = 3

Arranging both equations in standard form

3x + 4y = -6……(i) and 3x -y = 9…..(ii)

Subtracting equation (ii) from equation (i)

5y =-15

y = -3

Putting the value of y in equation (i)

3x + 4×-3 =-6

3x -12 = -6

3x = -6 +12 = 6

x = 2

Hence the value of x is 2 and value of y is -3

Similarly, you can do other parts of the question and study for the substitution method.

### NCERT Solutions for Class 10 Maths Exercise 3.4 of Chapter 3 Linear Equation in Two Variables

Q2. Form the pair of linear equations in the following problems, and find their solutions(if they exist) by elimination method:

(i) If we add 1 to the numerator and subtract 1 from the denominator,a fraction reduces to 1, it becomes 1/2 if we only add 1 to the denominator. What is the fraction?

Ans. Let the numerator is x and the denominator is y

According to the first condition

(x +1)/(y -1) = 1

x + 1 = y -1

x -y = -2……(i)

According to the second condition

x/(y+1) = 1/2

2x = y +1

2x -y = 1……(ii)

Multiplying the equation (i) by 2

2x -2y = -4….(iii)

Subtracting the equation (iii) from the equation (ii)

y =5

Putting the value of y  in equation (i)

x -5 =-2

x =-2 +5 =3

Hence the required fraction is 3/5

(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?

Ans. Let the age of Nuri is x and the age of Sonu is y

According to first condition

5 years back the age of Nuri = 3× 5 years back the age of Sonu

x -5 = 3(y -5)

x -5 = 3y -15

x – 3y = -10….(i)

According to second condition

10 years later the age of Nuri = 2× 10 years later the age of Sonu

x +10 = 2(y +10)

x +10= 2y +20

x +10= 2y +20

x -2y =10…..(ii)

Substracting the equation (ii) from the equation (i)

-y = -20

y = 20

Putting the value of y in equation (i)

x -3×20 = -10

x -60 = -10

x = -10 +60 = 50

Hence the age of Nuri is 50 years and the age of Sonu is 20 years

(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.

Ans. Let once of a two-digit number is x and tense of a two-digit number is y

∴ The number = 10y +x

According to the first condition

The sum of the digits = 9

x + y =9……(i)

9× The number = 2× The number obtained by reversing its digits

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

90y + 9x = 20x + 2y

90y -2y +9x -20x =0

88y -11x =0

8y -x =0…..(ii)

Substituting x = 8y from equation (ii) to equation (i)

8y +y = 9

9y =9

y =1

Putting the value of y in equation (i)

x + 1 = 9

x = 8

Hence the required number is 10y +x =10×1+ 8 = 18

### NCERT Solutions for Class 10 Maths Exercise 3.4 of Chapter 3 Linear Equation in Two Variables

(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.

Ans. Let the notes of Rs 50 are x and of Rs 100 are y

According to first condition

The notes of Rs 50 ×The number of Rs 50 notes +The notes of Rs 100 ×The number of Rs 100 notes = Rs 2000

50x + 100y =2000

x + 2y = 40…..(i)

According to second condition

The number of Rs 50 notes +The number of  Rs 100 notes =25

x + y =25…….(ii)

Subtracting equation (ii) from equation (i)

y = 15

Putting the value y =15 in equation (i)

x + 2×15 =40

x + 30 =40

x = 40 -30 = 10

Hence the Rs 50 notes are 10 and the Rs 100 notes are 15

(v) A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs.27 for a book kept for seven days, while Susy paid Rs.21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.

Ans.Let a lending library has a fixed charge of x for 3 days and charge y for each extra day.

According to the first condition, Saritha paid Rs 27 for a book kept for  7 days

Total charge = 3 days fixed charge + charge for (7 -3) days

27 = x + 4y

x + 4y =27….(i)

According to the second condition, Susy paid Rs.21 for the book she kept for five days

Total charge = 3 days fixed charge + charge for (5 -3) days

21 = x + 2y

x + 2y =21….(ii)

Subtracting equation (ii) from equation (i)

2y =6

y =3

Putting the value of y in equation (i)

x + 4×3 = 27

x +12 = 27

x = 15

Therefore the fixed charge for 3 days is Rs 15 and the charge for an extra day is Rs 3

You can compensate us by donating any amount of money for our survival

Our Paytm No 9891436286

#### NCERT Solutions for Class 10 Maths Exercise 3.1 to Exercise 3.7 Chapter 3 Pair of Linear Equations in Two Variables

Exercise 3.1

Exercise 3.2

Exercise 3.3

Exercise 3.4

Exercise 3.5

Exercise 3.6

Exercise 3.7

Class 10 maths NCERT solutions of important questions of chapter 3 Pair of Linear Equations

## NCERT Solutions of  Science and Maths for Class 9,10,11 and 12

### NCERT Solutions of class 9 maths

 Chapter 1- Number System Chapter 9-Areas of parallelogram and triangles Chapter 2-Polynomial Chapter 10-Circles Chapter 3- Coordinate Geometry Chapter 11-Construction Chapter 4- Linear equations in two variables Chapter 12-Heron’s Formula Chapter 5- Introduction to Euclid’s Geometry Chapter 13-Surface Areas and Volumes Chapter 6-Lines and Angles Chapter 14-Statistics Chapter 7-Triangles Chapter 15-Probability Chapter 8- Quadrilateral

### NCERT Solutions of class 9 science

 Chapter 1-Matter in our surroundings Chapter 9- Force and laws of motion Chapter 2-Is matter around us pure? Chapter 10- Gravitation Chapter3- Atoms and Molecules Chapter 11- Work and Energy Chapter 4-Structure of the Atom Chapter 12- Sound Chapter 5-Fundamental unit of life Chapter 13-Why do we fall ill ? Chapter 6- Tissues Chapter 14- Natural Resources Chapter 7- Diversity in living organism Chapter 15-Improvement in food resources Chapter 8- Motion Last years question papers & sample papers

CBSE Class 9-Question paper of science 2020 with solutions

CBSE Class 9-Sample paper of science

CBSE Class 9-Unsolved question paper of science 2019

### NCERT Solutions of class 10 maths

 Chapter 1-Real number Chapter 9-Some application of Trigonometry Chapter 2-Polynomial Chapter 10-Circles Chapter 3-Linear equations Chapter 11- Construction Chapter 4- Quadratic equations Chapter 12-Area related to circle Chapter 5-Arithmetic Progression Chapter 13-Surface areas and Volume Chapter 6-Triangle Chapter 14-Statistics Chapter 7- Co-ordinate geometry Chapter 15-Probability Chapter 8-Trigonometry

CBSE Class 10-Question paper of maths 2021 with solutions

CBSE Class 10-Half yearly question paper of maths 2020 with solutions

CBSE Class 10 -Question paper of maths 2020 with solutions

CBSE Class 10-Question paper of maths 2019 with solutions

### NCERT solutions of class 10 science

 Chapter 1- Chemical reactions and equations Chapter 9- Heredity and Evolution Chapter 2- Acid, Base and Salt Chapter 10- Light reflection and refraction Chapter 3- Metals and Non-Metals Chapter 11- Human eye and colorful world Chapter 4- Carbon and its Compounds Chapter 12- Electricity Chapter 5-Periodic classification of elements Chapter 13-Magnetic effect of electric current Chapter 6- Life Process Chapter 14-Sources of Energy Chapter 7-Control and Coordination Chapter 15-Environment Chapter 8- How do organisms reproduce? Chapter 16-Management of Natural Resources

### Solutions of class 10 last years Science question papers

CBSE Class 10 – Question paper of science 2020 with solutions

CBSE class 10 -Latest sample paper of science

### NCERT solutions of class 11 maths

 Chapter 1-Sets Chapter 9-Sequences and Series Chapter 2- Relations and functions Chapter 10- Straight Lines Chapter 3- Trigonometry Chapter 11-Conic Sections Chapter 4-Principle of mathematical induction Chapter 12-Introduction to three Dimensional Geometry Chapter 5-Complex numbers Chapter 13- Limits and Derivatives Chapter 6- Linear Inequalities Chapter 14-Mathematical Reasoning Chapter 7- Permutations and Combinations Chapter 15- Statistics Chapter 8- Binomial Theorem Chapter 16- Probability

CBSE Class 11-Question paper of maths 2015

CBSE Class 11 – Second unit test of maths 2021 with solutions

### NCERT solutions of class 12 maths

 Chapter 1-Relations and Functions Chapter 9-Differential Equations Chapter 2-Inverse Trigonometric Functions Chapter 10-Vector Algebra Chapter 3-Matrices Chapter 11 – Three Dimensional Geometry Chapter 4-Determinants Chapter 12-Linear Programming Chapter 5- Continuity and Differentiability Chapter 13-Probability Chapter 6- Application of Derivation CBSE Class 12- Question paper of maths 2021 with solutions Chapter 7- Integrals Chapter 8-Application of Integrals

.

Scroll to Top