NCERT Class Solutions
  • Home
  • 9th Solutions
    • Maths Solutions
    • Science Solutions
    • Social Science Solutions
  • 10th Solutions
    • Science Solutions
    • Maths Solutions
    • Social Science Solutions
    • English Solutions
    • Hindi Solutions
    • Sanskrit Solutions
  • NCERT Books
    • Class 10 Books PDF
    • Class 9 Books PDF
  • About Us
    • Write for Us
    • Contact Us
    • Privacy Policy
    • Disclaimer
  • MP Board
    • MP Board Solutions
    • Previous Year Papers
No Result
View All Result
  • Home
  • 9th Solutions
    • Maths Solutions
    • Science Solutions
    • Social Science Solutions
  • 10th Solutions
    • Science Solutions
    • Maths Solutions
    • Social Science Solutions
    • English Solutions
    • Hindi Solutions
    • Sanskrit Solutions
  • NCERT Books
    • Class 10 Books PDF
    • Class 9 Books PDF
  • About Us
    • Write for Us
    • Contact Us
    • Privacy Policy
    • Disclaimer
  • MP Board
    • MP Board Solutions
    • Previous Year Papers
No Result
View All Result
NCERT Class Solutions
No Result
View All Result
ADVERTISEMENT
Home Class 10th Solutions 10th Maths

NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5

by Sudhir
December 4, 2021
in 10th Maths, Class 10th Solutions
Reading Time: 9 mins read
0
NCERT Class 10th Maths Solutions
15
VIEWS
Share on FacebookShare on Twitter

In this post, we will share NCERT Class 10th Maths Book Solutions Pair of Linear Equations in Two Variables Ex 3.5. These solutions are based on new NCERT Syllabus.

NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5

Question 1.
Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method.
(i) x – 3y – 3 = 0; 3x – 9y – 2 = 0
(ii) 2x + y = 5; 3x + 2y = 8
(iii) 3x – 5y = 20; 6x -10y = 40
(iv) x – 3y – 7 = 0; 3x – 3y – 15 = 0
Solution:
(i) For x – 3y – 3 = 0, 3x – 9y – 2 = 0
∴ a1 = 1, b1 = – 3, C1 = – 3, a2 = 3, b2 = – 9, C2 = -2
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 1
∴ The given system has no solution.

(ii) 2x + y – 5 = 0, 3x + 2y – 8 = 0
∴ a1 = 2, b1 = 1, c1 = -5, a2 = 3, b2 = 2, c2 = -8
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 2
∴ The given system has a unique solution.
Now, using cross multiplication method, we have
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 3

(iii) For 3x – 5y – 20 = 0, 6x – 10y – 40 = 0
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 4
∴ The given system of linear equation has infinitely many solutions

(iv) For x – 3y – 7 = 0, 3x – 3y – 15 = 0
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 5
∴ The given statement has unique solution. Now, using cross multiplication method, we have
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 40

Question 2.
(i) For which values of a and b does the following pair of linear equations have an infinite number of solutions ?
2x + 3y = 7; (a – b) x + (a + b) y = 3a + b – 2
(ii) For which value of k will the following pair of linear equations have no solution ?
3x + y = 1; (2k – 1) x + (k – 1) y = 2k + 1
Solution:
(i) We have, 2x + 3y = 7 and
(a – b) x + (a + b) y = (3a + b – 2)
⇒ 2x + 3y – 7 = 0
and (a – b) x + (a + b) y -(3a + b – 2) = 0
a1 = 2, b1 = 3, c1 = – 7, a2 = (a- b) , b2 = (a + b) , c2 = -(3a + b – 2)
For infinite number of solutions,
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 6
From the first two equations, we get
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 7
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 8

NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5

Question 3.
Solve the following pair of linear equations by the substitution and cross-multiplication methods: 8x + 5y = 9; 3x + 2y = 4
Solution:
Method-1 [Substitution method]:
8x + 5y = 9 … (1)
3x + 2y = 4 … (2)
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 9

Question 4.
Form the pair of linear equations in the following problems and find their solutions (if they exist)by any algebraic method:
(i) A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay ₹ 1000 as hostel charges whereas a student B, who takes food for 26 days, pays ₹ 1180 as hostel charges. Find the fixed charges and the cost of food per day.
(ii) A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. Find the fraction.
(iii) Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?
(iv) Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?
(v) The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.
Solution:
(i) Let the fixed charges = ₹ x
and charges of food per day = ₹ y
For student A : Number of days = 20
∴ Cost of food for 20 days = ₹ 20y
According to the problem,
x + 20y = 1000
⇒ x + 20y – 1000 = 0 …. (1)
For student B : Number of days = 26
Cost of food for 26 days = ₹ 26y
According to the problem,
x + 26y = 1180
⇒ x + 26y – 1180 = 0 … (2)
Solving these by cross multiplication, we get
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 10
Thus x = 400 and y = 30
∴ Fixed charges = ₹ 400
and cost of food per day = ₹ 30

NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5

(ii) Let the numerator = x
and the denominator = y
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 11
From equations (1) and (2) , we have
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 12

NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5

(iii) Let the number of correct answers = ₹ x
and the number of wrong answers = ₹ y
Case-I: Marks for all correct answers
= (3 × x) = 3x
Mark for all wrong answers = (1 × y) = y
∴ According to the condition :
3x – y = 40 ⇒ 3x – y – 40 = 0
Case-II: Mark for all correct answers
= (4 × x)=
Marks for all wrong answers = (2 × y)
= 2y
∴ According to the condition :
4x – 2y = 50
⇒ 2x – y = 25 ⇒ 2x – y – 25 = 0 … (2)
From (1)and (2) , we have a1 = 3, b1 = -1, c1 = -40, a2 = 2, b2 = -1, c2 = -25
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 13
Now, total number of questions = [Number of correct answers] + [Number of wrong answers]
= 15 + 5 = 20
Thus, required number of questions = 20.

NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5

(iv) Let the speed of car-I be x km/hr.
and the speed of car-II be y km/hr.
Case-I:
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 14
Distance travelled by car-I = AC
∵ AC = time × speed = 5 × x km, AC = 5x
Distance travelled by car-II, BC = 5y
Since AB = AC – BC,
100 = 5x – 5y
⇒ 5x – 5y – 100 = 0
⇒ x – y – 20 = 0 …. (1)
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 15
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 16
Thus, speed of car-I = 60 km/hr
Speed of car-II = 40 km/hr

NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5

(v) Let the length of the rectangle = x units
and the breadth of the rectangle = y units
∴ Area of rectangle = x × y = xy
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 17
Condition-II:
(Length + 3) × (Breadth + 2) = Area + 67
⇒ (x + 3) (y + 2)= xy + 67 ⇒ 2x + 3y + 6 = 67
⇒ 2x + 3y – 61 = 0….(2)
Now, using cross multiplication method in (1)and (2) , where
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.5 18
Thus, length of the rectangle = 17 units and breadth of the rectangle = 9 units.

Previous Post

NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.3

Next Post

NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.6

Related

NCERT Class 10th Sanskrit Solutions
10th Sanskrit

Abhyasvan Bhav Sanskrit Class 10 Chapter 3 अनुच्छेदलेखमन्

NCERT Class 10th Sanskrit Solutions
10th Sanskrit

Abhyasvan Bhav Sanskrit Class 10 Chapter 4 चित्रवर्णनम्

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Categories

  • Books
    • Class 10 Books PDF
  • Class 10th Solutions
    • 10th English
    • 10th Hindi
    • 10th Maths
    • 10th Sanskrit
    • 10th Science
    • 10th Social Science
  • Class 9th Solutions
    • 9th Maths
    • 9th Science
    • 9th Social Science
  • MP Board
  • Uncategorized

Recent

NCERT Class 10th Sanskrit Solutions

Abhyasvan Bhav Sanskrit Class 10 Chapter 4 चित्रवर्णनम्

NCERT Class 10th Sanskrit Solutions

Abhyasvan Bhav Sanskrit Class 10 Chapter 3 अनुच्छेदलेखमन्

NCERT Class 10th Sanskrit Solutions

Abhyasvan Bhav Sanskrit Class 10 Chapter 2 पत्रलेखनम्

NCERT Class Solutions

We provide NCERT Solutions

NCERT Class Solutions App Play Store

Follow Us

Browse By Category

  • Books
    • Class 10 Books PDF
  • Class 10th Solutions
    • 10th English
    • 10th Hindi
    • 10th Maths
    • 10th Sanskrit
    • 10th Science
    • 10th Social Science
  • Class 9th Solutions
    • 9th Maths
    • 9th Science
    • 9th Social Science
  • MP Board
  • Uncategorized
  • Write for Us
  • Privacy Policy
  • Contact Us

© 2022 NCERT Class Solutions .

No Result
View All Result
  • Home
  • 9th Solutions
    • Maths Solutions
    • Science Solutions
    • Social Science Solutions
  • 10th Solutions
    • Science Solutions
    • Maths Solutions
    • Social Science Solutions
    • English Solutions
    • Hindi Solutions
    • Sanskrit Solutions
  • NCERT Books
    • Class 10 Books PDF
    • Class 9 Books PDF
  • About Us
    • Write for Us
    • Contact Us
    • Privacy Policy
    • Disclaimer
  • MP Board
    • MP Board Solutions
    • Previous Year Papers

© 2022 NCERT Class Solutions .

This website uses cookies. By continuing to use this website you are giving consent to cookies being used. Visit our Privacy and Cookie Policy.