NCERT Solutions for Class 9 Maths 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.

Linear Equations in Two Variables Class 9 – Exercise 4.2 Questions

If you are a student of class 9 and going to prepare for your examination and your school comes under the Central Board of Secondary Education then you must look at these solutions for NCERT Questions Class 9 Maths. NCERT Solutions are very helpful and it will help you to score good marks in the examination. In this study material, you will find all the contents as per the syllabus. The syllabus of class 9 Maths consists of 9 chapters. You will get immense help from the class 9 maths NCERT solutions chapter 4 exercise 4.2 content. The NCERT maths class 9 chapter 4 exercise 4.2 is beneficial for you for sure.

• The topics and subtopics in the first chapter which is Number System are Introduction to Number System, Irrational Numbers, Real Numbers and their Decimal Expansions, Representing Real Numbers on the Number Line, Operations on Real Numbers, Laws of Exponents for Real Numbers.

• The second chapter is Polynomials where you will learn about topics and subtopics like Polynomials in One Variable, Zeros of a Polynomial, Remainder Theorem, Factorisation of Polynomials and Algebraic Identities.

• Coordinate Geometry is the third chapter where you can learn some calculations like The relative position of an object present in a plane, distance between two bodies present in different planes, Location of points in the real dimension (X-Y-Z axis), Classification of a plane - division into axes, Calculating equations based on coordinate points.

• The NCERT Solutions for Class 9 Maths Chapter 4 is Linear Equations in Two Variables. The topics and subtopics are Linear Equations, Solution of a Linear Equation, Graph of a Linear Equation in Two Variables, Equations of Lines Parallel to the x-axis and y-axis. You can download free PDFs of NCERT Solution for Class 9 Maths Chapter 4 Exercise 4.2. You will not only be able to download the PDF of NCERT Solutions of Maths Class 9 Chapter 4 Exercise 4.2 but you can also download all the PDFs of other chapters and Exercises. Class 9th Maths NCERT Solutions Chapter 4 Exercise 4.2 will help to solve some calculations like how to write Linear Equations in Two Variables, how to express any linear equation in any form. From the NCERT Maths Solution Class 9 Chapter 4 Exercise 4.2 you will learn other calculations like draw graphs of Linear Equations in Two Variables, draw a line after plotting some points on the graph and many others. The NCERT solutions for class 9 maths chapter 4 exercise 4.2 has been tailored to help you solve all these problems with aplomb.

•  In the Exercise 4.2 Class 9 Maths, the first question is a multiple choice type. To answer the second question, students will have to write four solutions for each of the given questions. Maths NCERT Solutions Class 9 Chapter 4 Exercise 4.2 will help to clear all your doubts about the chapter because it's designed in that way. Chapter 4 maths class 9 exercise 4.2 will certainly help you get more marks.

• The fifth chapter of the syllabus Is Introduction to Euclid's Geometry where you will be learning about Euclid's Definitions, Axioms and Postulates, Equivalent Versions of Euclid's Fifth Postulate. You can look at the given exercises to solve your problems.

• The sixth chapter Lines and Angles deal with the basic geometrical application of angles and their relationships with lines where you will learn how angles are formed when two lines intersect each other and when one line intersects more than one parallel line at different points to form distinct angels.

• The topics and subtopics of the seventh chapter Triangles are Congruence of Triangles, Criteria for Congruence of Triangles, Some Properties of a Triangle, Some More Criteria for Congruence of Triangles, Inequalities in a Triangle.

• In the chapter eight, Quadrilaterals, you will know about how to find the angles of a given quadrilateral, prove a hypothesis and consider that the diagonal of a quadrilateral are equal and prove that it is a rectangle. You will learn that if the diagonals of a quadrilateral bisect at right angles then it can be established as a rhombus. You will also learn many shortcut techniques to solve the problems properly from NCERT Solutions.

• Areas of Parallelograms and Triangles is the 9th chapter and the topics and subtopics are Figures on the Same Base and Between the Same Parallels, Parallelograms on the Same Base and Between the Same Parallels, Triangles on the Same Base and Between the Same Parallels.

• The 10th chapter is Circle, and the topics and subtopics are Circles and its Related Terms; A Review, Angle Subtended by a Chord at a Point, Perpendicular from the Centre to a Chord, Circle through Three Points, Equal Chords and Their Distances from the Centre, Angle Subtended by an Arc of a Circle, Cyclic Quadrilaterals.

• Basic Constructions and Some Constructions of Triangles in chapter Eleven are the two topics in the eleventh chapter Constructions. To make this chapter easier, you can solve the exercises given in the book.

• The twelfth chapter Heron's Formula will give you an introduction of topics like Area of a Triangle - by Heron's Formula, Application of Heron's Formula in Finding Areas of Quadrilaterals. NCERT Solutions covers all the exercises of the chapters, you will get help from them also.

• The topics and subtopics of the chapter 13 Triangles are Surface Area of a Cuboid and a Cube, Surface Area of a Right Circular Cylinder, Surface Area of a Right Circular Cone, Surface Area of a Sphere, Volume of a Cuboid, Volume of a Cylinder, Volume of a Right Circular Cone, Volume of a Sphere.

• The chapter Statistics is the 14th chapter of the syllabus and the topics and subtopics are Collection of Data, Presentation of Data, Graphical Representation of Data, Measures of Central Tendency.

• The fifteenth and the last chapter is Probability. You need a clear idea of what Probability is to solve the problems of this chapter. Probability is the possible number of outcomes divided by the total number of outcomes. Probability is a part of Statistics. You can practice all the exercises where you will get the latest shortcut techniques to understand better.

Some Tips to Study Before the Examination

It is obvious that if you don't start from the beginning of your academic year then you will get too much pressure from studies before the examination. Mathematics is the subject where the key to success is practice. Try to solve some problems every day and if you find Maths is very tough then you will have to spend extra time on this subject.

Always keep a small diary or notebook with you, where you can note every math formula of your syllabus and important notes. This will help you to study effectively and you can look at this notebook whenever you forget something important about the subject. This will also help you with your last-minute preparation before the exam. And make sure that you have all the study materials in front of you on the study table so that you will not have to spend time in search of them.

Try to get up early in the morning and start your day with the study routine that you have created. You can study mathematics and science in the first few hours of the day if you find these subjects a little more difficult than the others. Don't get distracted from playing games or watching TV, try to avoid these things during the preparation or make a proper time table to these things after a full day study. Eat healthy foods and drink plenty of water and don't forget to have proper sleep at night as this can give you headaches. Don't try to clear your doubts before a few days of the examination, those days are for revision. If you have any doubts about anything then clear them with the help of Vedantu.

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