Class 10 Exam > Class 10 Notes > Mathematics (Maths) Class 10 > RD Sharma Solutions: Pair of Linear Equations in Two Variables - 3
Pair of Linear Equations in Two Variables - 3 RD Sharma Solutions | Mathematics (Maths) Class 10 PDF Download
| Download, print and study this document offline |
Please wait while the PDF view is loading
Page 1
Exercise 3.3
Solve the following systems of equations:
1. 11x + 15y + 23 = 0
7x – 2y – 20 = 0
Sol:
The given system of equation is
? ?
? ?
11 15 23 0 ...
7 2 20 0 ...
x y i
x y ii
? ? ?
? ? ?
From (ii), we get
2 7 20
7 20
2
yx
x
y
??
?
??
Substituting
7 20
2
x
y
?
? in (i) we get
7 20
11 15 23 0
2
105 300
11 23 0
2
22 105 300 46
0
2
127 254 0
127 254
254
2
127
x
x
x
x
xx
x
x
x
? ??
? ? ?
??
??
?
? ? ? ?
? ? ?
??
? ? ?
??
? ? ?
Page 2
Exercise 3.3
Solve the following systems of equations:
1. 11x + 15y + 23 = 0
7x – 2y – 20 = 0
Sol:
The given system of equation is
? ?
? ?
11 15 23 0 ...
7 2 20 0 ...
x y i
x y ii
? ? ?
? ? ?
From (ii), we get
2 7 20
7 20
2
yx
x
y
??
?
??
Substituting
7 20
2
x
y
?
? in (i) we get
7 20
11 15 23 0
2
105 300
11 23 0
2
22 105 300 46
0
2
127 254 0
127 254
254
2
127
x
x
x
x
xx
x
x
x
? ??
? ? ?
??
??
?
? ? ? ?
? ? ?
??
? ? ?
??
? ? ?
Putting 2 x ? in
7 20
2
x
y
?
? we get
7 2 20
2
14 20
2
6
2
3
y
??
??
?
?
?
?
??
Hence, the solution of the given system of equations is 2, 3. xy ? ? ?
2. 3x – 7y + 10 = 0
y – 2x – 3 = 0
Sol:
The given system of equation is
? ?
? ?
3 7 10 0 ...
2 3 0 ...
x y i
y x ii
? ? ?
? ? ?
From (ii), we get
23 yx ??
Substituting 23 yx ?? in (i) we get
? ? 3 7 2 3 10 0
3 14 21 10 0
11 11
11
1
11
xx
xx
x
x
? ? ? ?
? ? ? ? ?
? ? ?
? ? ? ?
?
Putting 1 x ?? in 2 3, yx ?? we get
? ? 2 1 3
23
1
1
y
y
? ? ? ? ?
? ? ?
?
??
Hence, the solution of the given system of equations is 1, 1. xy ? ? ?
3. 0.4x + 0.3y = 1.7
0.7x + 0.2y = 0.8
Sol:
Page 3
Exercise 3.3
Solve the following systems of equations:
1. 11x + 15y + 23 = 0
7x – 2y – 20 = 0
Sol:
The given system of equation is
? ?
? ?
11 15 23 0 ...
7 2 20 0 ...
x y i
x y ii
? ? ?
? ? ?
From (ii), we get
2 7 20
7 20
2
yx
x
y
??
?
??
Substituting
7 20
2
x
y
?
? in (i) we get
7 20
11 15 23 0
2
105 300
11 23 0
2
22 105 300 46
0
2
127 254 0
127 254
254
2
127
x
x
x
x
xx
x
x
x
? ??
? ? ?
??
??
?
? ? ? ?
? ? ?
??
? ? ?
??
? ? ?
Putting 2 x ? in
7 20
2
x
y
?
? we get
7 2 20
2
14 20
2
6
2
3
y
??
??
?
?
?
?
??
Hence, the solution of the given system of equations is 2, 3. xy ? ? ?
2. 3x – 7y + 10 = 0
y – 2x – 3 = 0
Sol:
The given system of equation is
? ?
? ?
3 7 10 0 ...
2 3 0 ...
x y i
y x ii
? ? ?
? ? ?
From (ii), we get
23 yx ??
Substituting 23 yx ?? in (i) we get
? ? 3 7 2 3 10 0
3 14 21 10 0
11 11
11
1
11
xx
xx
x
x
? ? ? ?
? ? ? ? ?
? ? ?
? ? ? ?
?
Putting 1 x ?? in 2 3, yx ?? we get
? ? 2 1 3
23
1
1
y
y
? ? ? ? ?
? ? ?
?
??
Hence, the solution of the given system of equations is 1, 1. xy ? ? ?
3. 0.4x + 0.3y = 1.7
0.7x + 0.2y = 0.8
Sol:
The given system of equation is
? ?
? ?
0.4 0.3 1.7 ...
0.7 0.2 0.8 ...
x y i
x y ii
??
??
Multiplying both sides of (i) and (ii), by 10, we get
? ?
? ?
4 3 17 ...
7 2 8 ...
x y iii
x y iv
??
??
From (iv), we get
7 8 2
82
7
7
xy
y
x
??
?
?
Substituting
82
7
y
x
?
? in (iii), we get
82
4 3 17
7
32 8
3 17
7
32 29 17 7
y
y
y
y
y
? ??
??
??
??
?
? ? ?
? ? ? ?
29 119 32
29 87
87
3
29
y
y
y
? ? ?
??
? ? ?
Putting 3 y ? in
82
,
7
y
x
?
? we get
8 2 3
7
x
??
?
86
7
14
7
2
?
?
?
?
Hence, the solution of the given system of equation is 2, 3. xy ??
4. 0.8
2
x
y ??
Sol:
0.8
2
x
y ??
Page 4
Exercise 3.3
Solve the following systems of equations:
1. 11x + 15y + 23 = 0
7x – 2y – 20 = 0
Sol:
The given system of equation is
? ?
? ?
11 15 23 0 ...
7 2 20 0 ...
x y i
x y ii
? ? ?
? ? ?
From (ii), we get
2 7 20
7 20
2
yx
x
y
??
?
??
Substituting
7 20
2
x
y
?
? in (i) we get
7 20
11 15 23 0
2
105 300
11 23 0
2
22 105 300 46
0
2
127 254 0
127 254
254
2
127
x
x
x
x
xx
x
x
x
? ??
? ? ?
??
??
?
? ? ? ?
? ? ?
??
? ? ?
??
? ? ?
Putting 2 x ? in
7 20
2
x
y
?
? we get
7 2 20
2
14 20
2
6
2
3
y
??
??
?
?
?
?
??
Hence, the solution of the given system of equations is 2, 3. xy ? ? ?
2. 3x – 7y + 10 = 0
y – 2x – 3 = 0
Sol:
The given system of equation is
? ?
? ?
3 7 10 0 ...
2 3 0 ...
x y i
y x ii
? ? ?
? ? ?
From (ii), we get
23 yx ??
Substituting 23 yx ?? in (i) we get
? ? 3 7 2 3 10 0
3 14 21 10 0
11 11
11
1
11
xx
xx
x
x
? ? ? ?
? ? ? ? ?
? ? ?
? ? ? ?
?
Putting 1 x ?? in 2 3, yx ?? we get
? ? 2 1 3
23
1
1
y
y
? ? ? ? ?
? ? ?
?
??
Hence, the solution of the given system of equations is 1, 1. xy ? ? ?
3. 0.4x + 0.3y = 1.7
0.7x + 0.2y = 0.8
Sol:
The given system of equation is
? ?
? ?
0.4 0.3 1.7 ...
0.7 0.2 0.8 ...
x y i
x y ii
??
??
Multiplying both sides of (i) and (ii), by 10, we get
? ?
? ?
4 3 17 ...
7 2 8 ...
x y iii
x y iv
??
??
From (iv), we get
7 8 2
82
7
7
xy
y
x
??
?
?
Substituting
82
7
y
x
?
? in (iii), we get
82
4 3 17
7
32 8
3 17
7
32 29 17 7
y
y
y
y
y
? ??
??
??
??
?
? ? ?
? ? ? ?
29 119 32
29 87
87
3
29
y
y
y
? ? ?
??
? ? ?
Putting 3 y ? in
82
,
7
y
x
?
? we get
8 2 3
7
x
??
?
86
7
14
7
2
?
?
?
?
Hence, the solution of the given system of equation is 2, 3. xy ??
4. 0.8
2
x
y ??
Sol:
0.8
2
x
y ??
And
7
10
2
y
x
?
?
72
2 1.6 10
2
x y and
xy
?
? ? ? ?
?
2 1.6 7 10 5 x y and x y ? ? ? ?
Multiply first equation by 10
10 20 16 10 5 7 x y and x y ? ? ? ?
Subtracting the two equations
15 9
93
15 5
3 6 2
1.6 2 1.6
5 5 5
y
y
x
?
??
??
? ? ? ? ?
??
??
Solution is
23
,
55
??
??
??
5. 7(y + 3) – 2 (x + 3) = 14
4(y – 2) + 3 (x – 3) = 2
Sol:
The given system of equations id
? ? ? ? ? ?
? ? ? ? ? ?
7 3 2 3 14 ...
4 2 3 3 2 ...
y x i
y x ii
? ? ? ?
? ? ? ?
From (i), we get
7 21 2 4 14
7 14 4 21 2
23
7
xx
yx
x
y
? ? ? ?
? ? ? ? ?
?
??
From (ii), we get
4 8 3 9 2 yx ? ? ? ?
? ?
4 3 17 2 0
4 3 19 0 ...
yx
y x iii
? ? ? ? ?
? ? ? ?
Substituting
23
7
x
y
?
? in (iii), we get
Page 5
Exercise 3.3
Solve the following systems of equations:
1. 11x + 15y + 23 = 0
7x – 2y – 20 = 0
Sol:
The given system of equation is
? ?
? ?
11 15 23 0 ...
7 2 20 0 ...
x y i
x y ii
? ? ?
? ? ?
From (ii), we get
2 7 20
7 20
2
yx
x
y
??
?
??
Substituting
7 20
2
x
y
?
? in (i) we get
7 20
11 15 23 0
2
105 300
11 23 0
2
22 105 300 46
0
2
127 254 0
127 254
254
2
127
x
x
x
x
xx
x
x
x
? ??
? ? ?
??
??
?
? ? ? ?
? ? ?
??
? ? ?
??
? ? ?
Putting 2 x ? in
7 20
2
x
y
?
? we get
7 2 20
2
14 20
2
6
2
3
y
??
??
?
?
?
?
??
Hence, the solution of the given system of equations is 2, 3. xy ? ? ?
2. 3x – 7y + 10 = 0
y – 2x – 3 = 0
Sol:
The given system of equation is
? ?
? ?
3 7 10 0 ...
2 3 0 ...
x y i
y x ii
? ? ?
? ? ?
From (ii), we get
23 yx ??
Substituting 23 yx ?? in (i) we get
? ? 3 7 2 3 10 0
3 14 21 10 0
11 11
11
1
11
xx
xx
x
x
? ? ? ?
? ? ? ? ?
? ? ?
? ? ? ?
?
Putting 1 x ?? in 2 3, yx ?? we get
? ? 2 1 3
23
1
1
y
y
? ? ? ? ?
? ? ?
?
??
Hence, the solution of the given system of equations is 1, 1. xy ? ? ?
3. 0.4x + 0.3y = 1.7
0.7x + 0.2y = 0.8
Sol:
The given system of equation is
? ?
? ?
0.4 0.3 1.7 ...
0.7 0.2 0.8 ...
x y i
x y ii
??
??
Multiplying both sides of (i) and (ii), by 10, we get
? ?
? ?
4 3 17 ...
7 2 8 ...
x y iii
x y iv
??
??
From (iv), we get
7 8 2
82
7
7
xy
y
x
??
?
?
Substituting
82
7
y
x
?
? in (iii), we get
82
4 3 17
7
32 8
3 17
7
32 29 17 7
y
y
y
y
y
? ??
??
??
??
?
? ? ?
? ? ? ?
29 119 32
29 87
87
3
29
y
y
y
? ? ?
??
? ? ?
Putting 3 y ? in
82
,
7
y
x
?
? we get
8 2 3
7
x
??
?
86
7
14
7
2
?
?
?
?
Hence, the solution of the given system of equation is 2, 3. xy ??
4. 0.8
2
x
y ??
Sol:
0.8
2
x
y ??
And
7
10
2
y
x
?
?
72
2 1.6 10
2
x y and
xy
?
? ? ? ?
?
2 1.6 7 10 5 x y and x y ? ? ? ?
Multiply first equation by 10
10 20 16 10 5 7 x y and x y ? ? ? ?
Subtracting the two equations
15 9
93
15 5
3 6 2
1.6 2 1.6
5 5 5
y
y
x
?
??
??
? ? ? ? ?
??
??
Solution is
23
,
55
??
??
??
5. 7(y + 3) – 2 (x + 3) = 14
4(y – 2) + 3 (x – 3) = 2
Sol:
The given system of equations id
? ? ? ? ? ?
? ? ? ? ? ?
7 3 2 3 14 ...
4 2 3 3 2 ...
y x i
y x ii
? ? ? ?
? ? ? ?
From (i), we get
7 21 2 4 14
7 14 4 21 2
23
7
xx
yx
x
y
? ? ? ?
? ? ? ? ?
?
??
From (ii), we get
4 8 3 9 2 yx ? ? ? ?
? ?
4 3 17 2 0
4 3 19 0 ...
yx
y x iii
? ? ? ? ?
? ? ? ?
Substituting
23
7
x
y
?
? in (iii), we get
23
4 3 19 0
7
8 12
3 19 0
7
8 12 21 133 0
29 145 0
29 145
145
5
29
x
x
x
x
xx
x
x
x
? ??
? ? ?
??
??
?
? ? ? ?
? ? ? ? ?
? ? ?
??
? ? ?
Putting 5 x ? in
23
,
7
x
y
?
? we get
2 5 7
7
y
??
?
10 3
7
7
7
1
1 y
?
?
?
?
??
Hence, the solution of the given system of equations is 5, 1. xy ??
6.
?? 7
+
?? 3
= 5
?? 2
-
?? 9
= 6
Sol:
The given system of equation is
? ?
? ?
5 ...
73
6 ...
29
xy
i
xy
ii
??
??
From (i), we get
37
5
21
3 7 105
3 105 7
105 7
3
xy
xy
xy
y
x
?
?
? ? ?
? ? ?
?
??
From (ii), we get
Read More
|
124 videos|457 docs|77 tests
|
FAQs on Pair of Linear Equations in Two Variables - 3 RD Sharma Solutions - Mathematics (Maths) Class 10
| 1. What is the definition of a pair of linear equations in two variables? |  |
Ans. A pair of linear equations in two variables is a set of two equations that involve two variables and are of degree one. The general form of such equations is ax + by = c, where a, b, and c are constants.
| 2. How can I solve a pair of linear equations in two variables? | |
Ans. There are several methods to solve a pair of linear equations in two variables, such as the substitution method, elimination method, and graphical method. The choice of method depends on the given equations and personal preference.
| 3. Is it always possible to find a solution for a pair of linear equations in two variables? | |
Ans. Not always. If the given pair of equations represents parallel lines, there will be no solution as parallel lines do not intersect. Similarly, if the equations represent the same line, there will be infinitely many solutions.
| 4. What is the importance of solving a pair of linear equations in two variables? | |
Ans. Solving a pair of linear equations in two variables helps in finding the common solution(s) of the equations. These solutions can be used to determine the values of the variables in real-life situations, such as finding the intersection point of two lines or solving problems related to cost and revenue.
| 5. Can a pair of linear equations in two variables have more than one solution? | |
Ans. Yes, a pair of linear equations in two variables can have infinitely many solutions. This happens when the equations represent the same line. In such cases, any point on the line will satisfy both equations, resulting in infinitely many solutions.
About this Document
|
4.77/5 Rating |
|
Nov 07, 2024 Last updated |
Document Description: RD Sharma Solutions: Pair of Linear Equations in Two Variables - 3 for Class 10 2024 is part of Mathematics (Maths) Class 10 preparation.
The notes and questions for RD Sharma Solutions: Pair of Linear Equations in Two Variables - 3 have been prepared according to the Class 10 exam syllabus. Information about RD Sharma Solutions: Pair of Linear Equations in Two Variables - 3 covers topics
like and RD Sharma Solutions: Pair of Linear Equations in Two Variables - 3 Example, for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for RD Sharma Solutions: Pair of Linear Equations in Two Variables - 3.
Introduction of RD Sharma Solutions: Pair of Linear Equations in Two Variables - 3 in English is available as part of our Mathematics (Maths) Class 10
for Class 10 & RD Sharma Solutions: Pair of Linear Equations in Two Variables - 3 in Hindi for Mathematics (Maths) Class 10 course.
Download more important topics related with notes, lectures and mock test series for Class 10
Exam by signing up for free. Class 10: Pair of Linear Equations in Two Variables - 3 RD Sharma Solutions | Mathematics (Maths) Class 10
Description
Full syllabus notes, lecture & questions for Pair of Linear Equations in Two Variables - 3 RD Sharma Solutions | Mathematics (Maths) Class 10 - Class 10 | Plus excerises question with solution to help you revise complete syllabus for Mathematics (Maths) Class 10 | Best notes, free PDF download
Information about RD Sharma Solutions: Pair of Linear Equations in Two Variables - 3
In this doc you can find the meaning of RD Sharma Solutions: Pair of Linear Equations in Two Variables - 3 defined & explained in the simplest way possible. Besides explaining types of
RD Sharma Solutions: Pair of Linear Equations in Two Variables - 3 theory, EduRev gives you an ample number of questions to practice RD Sharma Solutions: Pair of Linear Equations in Two Variables - 3 tests, examples and also practice Class 10
tests
|
Explore Courses for Class 10 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
Free
,Pair of Linear Equations in Two Variables - 3 RD Sharma Solutions | Mathematics (Maths) Class 10
,study material
,past year papers
,Previous Year Questions with Solutions
,Pair of Linear Equations in Two Variables - 3 RD Sharma Solutions | Mathematics (Maths) Class 10
,Summary
,practice quizzes
,Semester Notes
,Sample Paper
,mock tests for examination
,Objective type Questions
,ppt
,Extra Questions
,Exam
,Pair of Linear Equations in Two Variables - 3 RD Sharma Solutions | Mathematics (Maths) Class 10
,shortcuts and tricks
,video lectures
,Important questions
,MCQs
,Viva Questions
;
Additional Information about RD Sharma Solutions: Pair of Linear Equations in Two Variables - 3 for Class 10 Preparation
RD Sharma Solutions: Pair of Linear Equations in Two Variables - 3 Free PDF Download
The RD Sharma Solutions: Pair of Linear Equations in Two Variables - 3 is an invaluable resource that delves deep into the core of the Class 10 exam.
These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective.
With the help of these notes, you can grasp complex subjects quickly, revise important points easily,
and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner,
allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material,
or toppers' notes, this PDF has got you covered. Download the RD Sharma Solutions: Pair of Linear Equations in Two Variables - 3 now and kickstart your journey towards success in the Class 10 exam.
Importance of RD Sharma Solutions: Pair of Linear Equations in Two Variables - 3
The importance of RD Sharma Solutions: Pair of Linear Equations in Two Variables - 3 cannot be overstated, especially for Class 10 aspirants.
This document holds the key to success in the Class 10 exam.
It offers a detailed understanding of the concept, providing invaluable insights into the topic.
By knowing the concepts well in advance, students can plan their preparation effectively.
Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.
RD Sharma Solutions: Pair of Linear Equations in Two Variables - 3 Notes
RD Sharma Solutions: Pair of Linear Equations in Two Variables - 3 Notes offer in-depth insights into the specific topic to help you master it with ease.
This comprehensive document covers all aspects related to RD Sharma Solutions: Pair of Linear Equations in Two Variables - 3.
It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation.
Practice papers and question papers enable you to assess your progress effectively.
Additionally, the paper analysis provides valuable tips for tackling the exam strategically.
Access to Toppers' notes gives you an edge in understanding complex concepts.
Whether you're a beginner or aiming for advanced proficiency, RD Sharma Solutions: Pair of Linear Equations in Two Variables - 3 Notes on EduRev are your ultimate resource for success.
RD Sharma Solutions: Pair of Linear Equations in Two Variables - 3 Class 10 Questions
The "RD Sharma Solutions: Pair of Linear Equations in Two Variables - 3 Class 10 Questions" guide is a valuable resource for all aspiring students preparing for the
Class 10 exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
Study RD Sharma Solutions: Pair of Linear Equations in Two Variables - 3 on the App
Students of Class 10 can study RD Sharma Solutions: Pair of Linear Equations in Two Variables - 3 alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the RD Sharma Solutions: Pair of Linear Equations in Two Variables - 3,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of RD Sharma Solutions: Pair of Linear Equations in Two Variables - 3 is prepared as per the latest Class 10 syllabus.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup