Class 9 Exam > Class 9 Notes > Mathematics (Maths) Class 9 > Long Answer Type Questions: Linear Equations in Two Variables
Class 9 Maths Chapter 4 Question Answers - Linear Equations in Two Variables
Question 1. The following observed values of x and y are thought to satisfy a linear equation.
Draw the graph using the values of x and y as given in the above table.
At what points the graph of the linear equation cuts the x-axis?
Solution. Plotting the points (6, –2) and (–6, 6) and joining them we get the graph AB which is the required graph.
The graph AB cuts the x-axis at point C (3, 0) and the y-axis at point D (0, 2).
Question 2. The taxi fare in a town is ₹10 for the first kilometre and ₹ 6 per km for the subsequent distance. Taking the distance as ‘x’ km and total fare as ₹y, write a linear equation for this information, what will be the total fare for 15 km?
Solution:
∵ Total distance is x km.
Total fare = ₹y
∴ x = 1 + (x – 1) = First km + Subsequent distance
Since, fare the first km = ₹10
∴ Fare for the remaining distance = ₹6 x (x – 1) = ₹6x – ₹6
⇒ Total fare = ₹10 + ₹6x – ₹6
= ₹4 + ₹6x
∴ y = 4 + 6x
⇒ y – 6x = 4
⇒ 6x – y + 4 = 0
Which is the required equation.
Now, total fare for 15 km:
6 x 15 – y + 4 = 0 [Substituting x = 15]
⇒ 90 – y + 4 = 0
⇒ 94 – y = 0
⇒ y = 94
∴ Total fare = ₹94.
Question 3. Draw the graph of the equation x – y = 4. From the graph, find the coordinates of the point when the graph line meets the x-axis.
Solution: We have x – y = 4 or y = x – 4
When x = 0, then y = 0 – 4 = –4
When x = 1, then y = 1 – 4 = –3
When x = –1, then y = – 1 – 4 = – 5
We get the following table of values of x and y.
x | 0 | 1 | -1 |
y | -4 | -3 | -5 |
(x, y) | (0, –4) | (1, –3) | (–1, –5) |
∴ We have the ordered pairs of solution for x – y = 4 as (0, –4), (1, –3) and (–1, –5).
Now, plotting the points (0, –4), (1, –3) and (–1, –5) and then joining them, we get the following graph of x – y = 4.
From the graph, we find that the graph line meets the x-axis at (4, 0).
Question 4. Draw the graph x + 2y = 6 and from the graph, find the value of x when y = – 3.
Solution: We have: x + 2y = 6
⇒ 
When x = 0, then 
When x = 2, then 
When x = 4, then 
We get the following table of values of x and y.
x | 0 | 2 | 4 |
y | 3 | 2 | 1 |
(x, y) | (0, 3) | (2, 2) | (4, 1) |
Plotting the ordered pairs (0, 3), (2, 2) and (4, 1) and then joining them, we get the graph of x + 2y = 6 as shown below:
From the graph, we find that for y = – 3, the value of x = 12.
The document Class 9 Maths Chapter 4 Question Answers - Linear Equations in Two Variables is a part of the Class 9 Course Mathematics (Maths) Class 9.
All you need of Class 9 at this link: Class 9
|
44 videos|412 docs|55 tests
|
FAQs on Class 9 Maths Chapter 4 Question Answers - Linear Equations in Two Variables
| 1. What are linear equations in two variables? |  |
Ans. Linear equations in two variables are algebraic equations that involve two variables, typically denoted as x and y, and have a degree of 1. These equations can be represented by straight lines on a coordinate plane and have the general form of ax + by = c, where a, b, and c are constants.
| 2. How do you solve a system of linear equations in two variables? | |
Ans. To solve a system of linear equations in two variables, you can use one of the following methods:
- Substitution method: Solve one equation for one variable and substitute it into the other equation.
- Elimination method: Multiply one or both equations by suitable constants to make the coefficients of one variable the same. Then, subtract or add the equations to eliminate one variable.
- Graphical method: Plot the equations on a coordinate plane and find the point of intersection, which represents the solution.
| 3. What is the importance of linear equations in two variables? | |
Ans. Linear equations in two variables have several applications in real-life situations. Some of the key importance of these equations are:
- They help in solving problems involving two unknowns, such as finding the cost and quantity of goods, determining the relationship between two variables, etc.
- They provide a mathematical model for various scientific and engineering problems, allowing for prediction and analysis.
- They form the basis for learning higher-level concepts in algebra and calculus, making them essential for further mathematical studies.
| 4. Can a linear equation in two variables have infinitely many solutions? | |
Ans. Yes, a linear equation in two variables can have infinitely many solutions. This occurs when the two equations represent the same line or are parallel to each other. In such cases, every point on the line is a solution to the system of equations. Graphically, these lines will coincide or never intersect, indicating infinite solutions.
| 5. How can linear equations in two variables be used to solve word problems? | |
Ans. Linear equations in two variables can be used to solve various word problems involving real-life scenarios. By assigning variables to unknown quantities and translating the problem into equations, we can solve for the desired values. For example, these equations can be used to find the cost and quantity of items, determine the speed and time of travel, analyze the relationship between two variables, and much more. The solutions obtained from the equations provide a mathematical representation of the problem and aid in making informed decisions.
About this Document
|
1.5K Views |
|
4.61/5 Rating |
|
Nov 22, 2024 Last updated |
Document Description: Long Answer Type Questions: Linear Equations in Two Variables for Class 9 2024 is part of Mathematics (Maths) Class 9 preparation.
The notes and questions for Long Answer Type Questions: Linear Equations in Two Variables have been prepared according to the Class 9 exam syllabus. Information about Long Answer Type Questions: Linear Equations in Two Variables covers topics
like and Long Answer Type Questions: Linear Equations in Two Variables Example, for Class 9 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Long Answer Type Questions: Linear Equations in Two Variables.
Introduction of Long Answer Type Questions: Linear Equations in Two Variables in English is available as part of our Mathematics (Maths) Class 9
for Class 9 & Long Answer Type Questions: Linear Equations in Two Variables in Hindi for Mathematics (Maths) Class 9 course.
Download more important topics related with notes, lectures and mock test series for Class 9
Exam by signing up for free. Class 9: Class 9 Maths Chapter 4 Question Answers - Linear Equations in Two Variables
Description
Full syllabus notes, lecture & questions for Class 9 Maths Chapter 4 Question Answers - Linear Equations in Two Variables - Class 9 | Plus excerises question with solution to help you revise complete syllabus for Mathematics (Maths) Class 9 | Best notes, free PDF download
Information about Long Answer Type Questions: Linear Equations in Two Variables
In this doc you can find the meaning of Long Answer Type Questions: Linear Equations in Two Variables defined & explained in the simplest way possible. Besides explaining types of
Long Answer Type Questions: Linear Equations in Two Variables theory, EduRev gives you an ample number of questions to practice Long Answer Type Questions: Linear Equations in Two Variables tests, examples and also practice Class 9
tests
|
Explore Courses for Class 9 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
practice quizzes
,Viva Questions
,Sample Paper
,MCQs
,ppt
,Objective type Questions
,Semester Notes
,Summary
,Extra Questions
,Important questions
,study material
,Class 9 Maths Chapter 4 Question Answers - Linear Equations in Two Variables
,video lectures
,Class 9 Maths Chapter 4 Question Answers - Linear Equations in Two Variables
,shortcuts and tricks
,Free
,past year papers
,mock tests for examination
,Previous Year Questions with Solutions
,Class 9 Maths Chapter 4 Question Answers - Linear Equations in Two Variables
,Exam
;
Additional Information about Long Answer Type Questions: Linear Equations in Two Variables for Class 9 Preparation
Long Answer Type Questions: Linear Equations in Two Variables Free PDF Download
The Long Answer Type Questions: Linear Equations in Two Variables is an invaluable resource that delves deep into the core of the Class 9 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 Long Answer Type Questions: Linear Equations in Two Variables now and kickstart your journey towards success in the Class 9 exam.
Importance of Long Answer Type Questions: Linear Equations in Two Variables
The importance of Long Answer Type Questions: Linear Equations in Two Variables cannot be overstated, especially for Class 9 aspirants.
This document holds the key to success in the Class 9 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.
Long Answer Type Questions: Linear Equations in Two Variables Notes
Long Answer Type Questions: Linear Equations in Two Variables Notes offer in-depth insights into the specific topic to help you master it with ease.
This comprehensive document covers all aspects related to Long Answer Type Questions: Linear Equations in Two Variables.
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, Long Answer Type Questions: Linear Equations in Two Variables Notes on EduRev are your ultimate resource for success.
Long Answer Type Questions: Linear Equations in Two Variables Class 9
The "Long Answer Type Questions: Linear Equations in Two Variables Class 9 Questions" guide is a valuable resource for all aspiring students preparing for the
Class 9 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 Long Answer Type Questions: Linear Equations in Two Variables on the App
Students of Class 9 can study Long Answer Type Questions: Linear Equations in Two Variables alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Long Answer Type Questions: Linear Equations in Two Variables,
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 Long Answer Type Questions: Linear Equations in Two Variables is prepared as per the latest Class 9 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