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 3.6

by Sudhir
December 4, 2021
in 10th Maths, Class 10th Solutions
Reading Time: 8 mins read
0
NCERT Class 10th Maths Solutions
21
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 3.6. These solutions are based on new NCERT Syllabus.

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

Question 1.
Solve the following pairs of equations by reducing them to a pair of linear equations:
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.6 23
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.6 24
Solution:
(i) we have
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.6 3
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.6 4
Equations (1) and (2) becomes,
2u + 3v = 2 ⇒ 2u + 3v – 2 = 0 … (3)
4u – 9v = -1 ⇒ 4u – 9v + 1 = 0 … (4)
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.6 5

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

(iii)
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.6 6
The equations (1) and (2) becomes,
4p + 3y = 14 ⇒ 4y + 3y -14 = 0 …. (3)
3p – 4y = 23 ⇒ 3p – 4y – 23 = 0 …. (4)
Here, a1 = 4, b1= 3, c1 = —14, a2 = 3, b2 = – 4, c2 = -23
Solving (3) and (4) by cross multiplication method, we get
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.6 7

(iv)
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.6 9
Equations (1) and (2) can be expressed
5u + v = 2 ⇒ 5u + v – 2 = 0 …. (3)
6u – 3v = 1 ⇒ 6u – 3v – 1 = 0 …. (4)
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.6 10
Thus, the required solution is x = 4, y = 5

(v)
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.6 11
∴ Equation (3)and (4)can be expressed as:
7q – 2p – 5 = 0 … (5)
8q + 7p -15 = 0 … (6)
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.6 12
Thus, the required solution is x = 1, y = 1

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

(vi) We have, 6x + 3y = 6xy …. (1)
2x + 4y = 5xy … (2)
From (1) , we get
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.6 13
2q + 4p = 5 ….(6)
Multiply (6) by 3, we get
6q +12p = 15 … (7)
Subtracting (5) from (7) , we get
6q + 12p – 6q – 3p = 15 – 6
9p = 9 ⇒ p = 1
Now, Substituting, p = 1 in (5) , we get
6q + 3(1) = 6
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.6 14
∴ Equations (1) and (2) can be expressed as :
10p + 2q = 4 = ⇒ 10p + 2q – 4 = 0 …(3)
15p – 5q = -2 ⇒ 15p – 5q + 2 = 0 … (4)
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.6 15
⇒ 2x = 6 ⇒ x = 3
Now, substituting the value of x in equation (5) , we get
3 + y = 5 ⇒ y = 2
Thus, the required solution is x = 3, y = 2

(viii)
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.6 16

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

Question 2.
Formulate the following problems as a pair of equations, and hence find their solutions:
(i) 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.
(ii) 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.
(iii) 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.
Solution:
(i) Let the speed of Ritu in still water = x km/hr
and the speed of the current = y km/hr
∴ Downstream speed = (x + y) km/hr
Upstream speed = (x – y)km/hr
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.6 17
Substituting the value of x in equation (1), we get
6 + y = 10 ⇒ y = 10 – 6 = 4
Thus, speed of rowing in still water = 6 km/hr, speed of current = 4 km/hr

(ii) Let the time taken to finish the task by one woman alone = x days
and the time taken to finish the task by one man alone = y days
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.6 18
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.6 19
∴ 1 man can finish the work in 36 days and 1 woman can finish the work in 18 days,

(iii) Let the speed of the train = x km/hr
and the speed of the bus = y km/hr
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.6 20
Case I: Total journey = 300 km
Distance travelled by train = 60 km
Distance travelled by bus = (300 – 60)km
= 240 km
∵ Total time taken = 4 hours
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.6 21

Case II: Distance travelled by train = 100 km
Distance travelled by bus = (300 – 100)km
= 200 km
Total time = 4 hrs 10 mins
NCERT Class 10th Maths Solutions Chapter 3 Pair of Linear Equations in Two Variables Ex 3.6 22
Thus, speed of the train = 60 km/hr
and speed of the bus = 80 km/hr

Previous Post

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

Next Post

NCERT Class 10th Maths Solutions Chapter 3 दो चरों वाले रैखिक समीकरण युग्म Examples and MCQs

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.