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NCERT Solutions for Class 9 Maths Chapter 4 - Linear Equations in Two Variables Exercise 4.2

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NCERT Solutions for Class 9 Maths Chapter 4 Exercise 4.2 - Free PDF Download

Class 9 Maths Chapter 4 exercise 4.2 Solutions focuses on solving linear equations in two variables. This essential part of algebra helps students understand how to handle equations with two unknowns. The important aspect here is to learn how to graph these equations and find solutions that satisfy both equations simultaneously.

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Table of Content
1. NCERT Solutions for Class 9 Maths Chapter 4 Exercise 4.2 - Free PDF Download
2. Glance of NCERT Solutions Class 9 Maths 4.2 Exercise Chapter 4 | Vedantu
3. Access NCERT Solutions for Maths Class 9 Chapter 4 - Linear Equations in Two Variables
4. NCERT Solution Class 9 Maths of Chapter 4 all Exercises
5. CBSE Class 9 Maths Chapter 4 Other Study Materials
6. Chapter-Specific NCERT Solutions for Class 9 Maths
FAQs


The key focus should be understanding the graphical method of solving equations, which involves plotting lines on a graph. The NCERT of Ex 4.2 class 9 also helps in visualising the solutions, making it easier to comprehend how equations interact. By mastering these concepts, students can tackle more complex problems with confidence.


You can download the FREE PDF for NCERT Solutions for Class 9 Maths from Vedantu and boost your preparations for Exams. 


Glance of NCERT Solutions Class 9 Maths 4.2 Exercise Chapter 4 | Vedantu

  • Linear Equation in Two Variables: An equation involving two variables (usually denoted by x and y) connected by linear operations (addition, subtraction, multiplication by a constant) where the highest power of any variable is 1.

  • Solution of a Linear Equation: A pair of values (x, y) that satisfies the equation. When you plug these values into the equation, both sides become equal.

  • Verifying Solutions: This exercise gives you equations and asks you to check if particular points (x, y) are solutions. Substitute the x and y values into the equation. If both sides become equal, the point is a solution.

  • Graphical Representation: Some questions ask you to analyse if a given equation has infinitely many solutions, no solutions, or a unique solution based on its graphical representation.

  • Infinitely Many Solutions: A linear equation represents a straight line. If the equation is of the form y = mx + c (where m and c are constants), it has infinitely many solutions because for every x value, there's a corresponding y value on the line.

  • No Solutions: Equations like x + y = 17 and 2x + 2y = 20 (lines that never intersect) have no solutions.

  • Unique Solution: Two intersecting lines have a unique point of intersection, which is the solution of the corresponding equations.

  • There are four questions in Class 9 Maths Ex 4.2 which are fully solved by experts at Vedantu.

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Access NCERT Solutions for Maths Class 9 Chapter 4 - Linear Equations in Two Variables

Exercise 4.2

1. Which one of the Following Options is True, and Why? \[\text{y=3x+5}\] has  

(i) A unique solution, 

(ii) only two solutions, 

(iii) infinitely many solutions

Ans. We are given that \[y=3x+5\] is a linear equation. 

  • For \[x=0\] , \[y=5\] . Therefore, \[(0,5)\] is a solution of the equation. 

  • For \[x=1\] , \[y=8\] . Therefore \[(1,8)\] is another solution of the equation. 

  • For \[x=2\] , \[y=11\] . Therefore \[(2,11)\] is another solution of the equation. 

Clearly, for different values of \[x\] , we get another distinct value of \[y\] .  

So, there is no end to different solutions of a linear equation in two variables. Therefore, a linear equation in two variables has infinitely many solutions.

Hence (iii) is the correct answer.  

2. Write Four Solutions for Each of the Following Equations:

(i) \[\text{2x+y=7}\]

Ans. Given equation \[2x+y=7\] , can be written as,

\[y=7-2x\]

Let us now take different values of \[x\] and substitute in the above equation-

  • For \[x=0\] ,

\[y=7\]

So, \[(0,7)\] is a solution.

  • For \[x=1\] ,

\[y=5\]

So, \[(1,5)\] is a solution.

  • For \[x=2\] ,

\[y=3\]

So, \[(2,3)\] is a solution.

  • For \[x=3\] ,

\[y=1\]

So, \[(3,1)\] is a solution.

Therefore, the four solutions of \[2x+y=7\] are \[(0,7)\] , \[(1,5)\] , \[(2,3)\] , \[(3,1)\] .

(ii) \[\pi \text{x+y=9}\]

Ans. Given equation \[\pi x+y=9\] , can be written as,

\[y=9-\pi x\]

Let us now take different values of \[x\] and substitute in the above equation-

  • For \[x=0\] ,

\[y=9\]

So, \[(0,9)\] is a solution.

  • For \[x=1\] ,

\[y=9-\pi \]

So, \[(1,9-\pi )\] is a solution.

  • For \[x=2\] ,

\[y=9-2\pi \]

So, \[(2,9-2\pi )\] is a solution.

  • For \[x=3\] ,

\[y=9-3\pi \]

So, \[(3,9-3\pi )\] is a solution.

Therefore, the four solutions of \[\pi x+y=9\] are \[(0,9)\] , \[(1,9-\pi )\] , \[(2,9-2\pi )\] , \[(3,9-3\pi )\] .

(iii) \[\text{x=4y}\]

Ans. Given equation \[x=4y\] .

Let us now take different values of \[y\] and substitute in the above equation-

  • For \[y=0\] ,

\[x=0\]

So, \[(0,0)\] is a solution.

  • For \[y=1\] ,

\[x=4\]

So, \[(4,1)\] is a solution.

  • For \[y=2\] ,

\[x=8\]

So, \[(8,2)\] is a solution.

  • For \[y=3\] ,

\[x=12\]

So, \[(12,3)\] is a solution.

Therefore, the four solutions of \[x=4y\] are \[(0,0)\] , \[(4,1)\] , \[(8,2)\] , \[(12,3)\].

3. Check Which of the Following are Solutions of the Equation \[x-2y=4\] and Which are not:

(i) \[(0,2)\]

Ans. Substituting \[x=0\] and \[y=2\] in the L.H.S. of the given equation \[x-2y=4\] :

\[\Rightarrow 0-2(2)\]

\[\Rightarrow -4\]

Since \[L.H.S.\ne R.H.S.\] , therefore \[(0,2)\] is not a solution of the equation.

(ii) \[(2,0)\]

Ans. Substituting \[x=2\] and \[y=0\] in the L.H.S. of the given equation \[x-2y=4\] :

\[\Rightarrow 2-2(0)\]

\[\Rightarrow 2\]

Since \[L.H.S.\ne R.H.S.\] , therefore \[(2,0)\] is not a solution of the equation.

(iii) \[(4,0)\]

Ans. Substituting \[x=4\] and \[y=0\] in the L.H.S. of the given equation \[x-2y=4\] :

\[\Rightarrow 4-2(0)\]

\[\Rightarrow 4\]

Since \[L.H.S.=R.H.S.\] , therefore \[(4,0)\] is a solution of the equation.

(iv) \[(\sqrt{2},4\sqrt{2})\]

Ans. Substituting \[x=\sqrt{2}\] and \[y=4\sqrt{2}\] in the L.H.S. of the given equation \[x-2y=4\] :

\[\Rightarrow \sqrt{2}-2(4\sqrt{2})\]

\[\Rightarrow -7\sqrt{2}\]

Since \[L.H.S.\ne R.H.S.\] , therefore \[(\sqrt{2},4\sqrt{2})\] is not a solution of the equation.

(v) \[(1,1)\]

Ans. Substituting \[x=1\] and \[y=1\] in the L.H.S. of the given equation \[x-2y=4\] :

\[\Rightarrow 1-2(1)\]

\[\Rightarrow -1\]

Since \[L.H.S.\ne R.H.S.\] , therefore \[(1,1)\] is not a solution of the equation.

4. Find the value of \[k\] , if \[x=2\] , \[y=1\] is a solution of the equation \[2x+3y=k\] .

Ans. We are given the equation \[2x+3y=k\] along with the values \[x=2\] and \[y=1\] .

Substituting the given values in the L.H.S. of the equation:

\[\Rightarrow 2(2)+3(1)=k\]

\[\Rightarrow 4+3=k\]

\[\Rightarrow k=7\]

Therefore, we get \[k=7\] on solving the equation.


Conclusion

NCERT of Class 9 maths exercise 4.2 focuses on Linear Equations in Two Variables, primarily dealing with understanding and solving linear equations by finding pairs of values that satisfy the given equations. It emphasizes graphing solutions and interpreting the relationships between variables. By practicing these problems, students learn to visualize equations and improve their problem-solving skills, preparing them for more complex algebraic concepts in Class 9th maths chapter 4 exercise 4.2. The solutions provided by Vedantu offer step-by-step explanations and can be a valuable resource for students aiming to clear their doubts and perform well in exams.


NCERT Solution Class 9 Maths of Chapter 4 all Exercises

Exercise

Number of Questions

Exercise 4.1

2 Questions & Solutions


CBSE Class 9 Maths Chapter 4 Other Study Materials


Chapter-Specific NCERT Solutions for Class 9 Maths

Given below are the chapter-wise NCERT Solutions for Class 9 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.


FAQs on NCERT Solutions for Class 9 Maths Chapter 4 - Linear Equations in Two Variables Exercise 4.2

1. What are the Solutions of Linear equation in 2 variables on a graph?

The  Solutions of Linear equation in 2 variables on a graph will be : 

  • Any linear equation in the standard form ax+by+c=0 has a pair of solutions (x,y), that can be represented in the coordinate plane.

  • When an equation is represented graphically, it is a straight line that may or may not cut the coordinate axes.

  • A linear equation ax+by+c=0 is represented graphically as a straight line.

  • Every point on the line is a solution for the linear equation.

  • Every solution of the linear equation is a point on the line.

2. when do a pair of linear equations with two variables have no solution.

If the two linear equations have equal slope value, then the equations will have no solutions.


m1 = m2. This is because the lines are parallel to each other and do not intersect.

3. What happens to Linear equation in 2 variables when (i) Lines passing through the origin (ii) Lines parallel to coordinate axes.

In a Linear equation in 2 variables


(i) Lines Passing Through the Origin

  • Certain linear equations exist such that their solution is (0,0). Such equations when represented graphically pass through the origin.

  • The coordinate axes x-axis and y-axis can be represented as y=0 and x=0 respectively.

(ii) Lines Parallel to Coordinate Axes

  • Linear equations of the form y=a, when represented graphically are lines parallel to the x-axis and a is the y-coordinate of the points in that line.

  • Linear equations of the form x=a, when represented graphically are lines parallel to the y-axis and a is the x-coordinate of the points in that line.

4. How to score well in Algebra?

Algebra is most students' scoring friend. Unlike arithmetic and geometry it does not have any theorems to prove or complicated word problems. Most of the problems in algebra can be solved through logic. Students can develop this logical thinking through repeated practise of algebra problems. Along with this students will have to know basic formulas of algebra and some popular algebraic expressions. All these combined together will help students to score effectively and efficiently high marks in maths. Along with these, students can also refer the follows study materials in order to be able to score well in algebra as well as overall in Maths: 

  • Previous Year Question Papers

  • Exemplar Solutions

  • NCERT Solutions 

  • Sample Papers

All the above study materials are provided by Vedantu as free PDF for the students to download. These study resources are curated keeping in mind the need for the students to understand maths rather than just mugging it up.

5. Is NCERT enough for Chapter 4 of Class 9 Maths?

You should strictly adhere to the NCERT book and complete all the exercises of Chapter 4 of Class 9 Maths. You should also review the NCERT questions and go through the solved examples in the chapter to ensure that there are no errors. To guarantee more precision and less room for error, use the NCERT Solutions for Chapter 4 Class 9 Maths available free of cost. If you still have time, you can go over some questions from the supplemental reference books.

6. How to make notes of Chapter 4 of Class 9 Maths?

Make notes in a clear, readable handwriting that contains all equations, definitions, theorems, solved examples, and NCERT exercises. It won't take long if you finish it while preparing for your test. Also, make certain that your notebook is in good functioning order so that you can refer to it if you have a doubt or need to study for the exam. Also refer to the NCERT Solutions and other study material available on Vedantu app and website, to be thorough with Chapter 4 of Class 9 Maths.

7. How to study for Class 9 Maths Chapter 4?

Before you start solving the questions in Chapter 4 of Class 9 Maths, read it thoroughly and compile a list of the statements, definitions, and theorems found within. This is important because we frequently focus just on the issues and ignore the theoretical aspects of mathematics. You will receive straight marks on the theoretical section of the test. If you understand the keywords and use them in your answers, you will earn full credit.

8. How to ensure full marks in Maths Class 9 Chapter 4?

Once you've finished your curriculum, you should practise the question papers of this chapter from prior sessions' examinations. This does not imply that you should start any question paper at the last minute. You should begin practising the previous year's questions if you have a solid understanding of Chapter 4. You must review your work when you have completed it to identify where you are missing. Seeing your mistakes motivates you to fix them and consider how you might avoid them in the main exam.

9. How to plan a study schedule for Chapter 4 of Class 9 Maths?

To plan a study schedule, you must first prepare a list of your priorities and what you find difficult. This can be done according to the weightage each chapter carries and then you must focus on the difficult chapter with more weightage of marks. Then prepare a relevant schedule that will meet your needs and change it as you progress through the syllabus. Which is to say that when you complete the syllabus, you can devote more time to revisions and so on. Before going on to the chapter assignments, you must first practise by working through the NCERT book's solved examples. You'll gradually master this approach and gain a deeper understanding of how concepts form and then score great marks in your examination.

10. What are the main concepts covered in Exercise 4.2?

In class 9 Ex 4.2 focuses on solving linear equations in two variables. It involves plotting these equations on a graph, finding the solutions of the equations graphically, and understanding the relationship between the algebraic and graphical representations of the equations.

11. How can we graph a linear equation in two variables?

To graph a linear equation in two variables, first, find at least two solutions of the equation. Plot these solutions as points on the coordinate plane. Then, draw a straight line through these points, which represents the graph of the equation.

12. What is the significance of the point of intersection of two lines?

The point of intersection of two lines representing linear equations in two variables is the solution to the system of equations. It indicates the values of the variables that satisfy both equations simultaneously. If the lines intersect at a single point, the system has a unique solution.