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NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations In Two Variables Ex 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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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. 

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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.



Important Study Materials for CBSE Class 9 Maths

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FAQs on NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations In Two Variables Ex 4.2

1. What are NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables?

NCERT Solutions for Class 9 Maths Chapter 4 are step-by-step explanations of all exercises, including Ex 4.2, that guide students through the CBSE methodology of solving linear equations in two variables. These solutions focus on reasoning, calculation steps, and understanding solution sets as per the latest CBSE 2025–26 syllabus.

2. How do you solve a linear equation in two variables in Class 9 Maths Ex 4.2?

To solve a linear equation in two variables, assign any value to one variable and solve for the other. This generates a set of ordered pairs (x, y) that satisfy the equation, which can be plotted to obtain a straight line on the coordinate plane.

3. How do NCERT Solutions help with graphing linear equations in two variables?

NCERT Solutions for Chapter 4 guide students in plotting at least two solution points of the equation on a graph, connecting them to form a straight line. Each point on the line represents a solution, visually demonstrating the infinite number of solutions possible for such equations.

4. What is the significance of the point of intersection between two linear equations in two variables?

The point of intersection on the graph represents the unique solution to both equations, meaning it is the pair of values that simultaneously satisfies both linear equations.

5. Can a linear equation in two variables have exactly one solution?

No. A linear equation in two variables has infinitely many solutions, as for each value of one variable, there is a corresponding value of the other variable that satisfies the equation.

6. When do two linear equations in two variables have no solution according to Class 9 NCERT Solutions?

Two linear equations in two variables have no solution if their graphs are parallel lines, i.e., their slopes are equal but their intercepts differ. This means the lines never meet.

7. What are the main concepts covered in Class 9 Maths Chapter 4 Exercise 4.2 NCERT Solutions?

Exercise 4.2 covers:

  • Generating and verifying solution pairs for linear equations.
  • Using the graphical method to represent solutions.
  • Testing if given pairs satisfy given equations.
All steps follow CBSE's prescribed approach for 2025–26.

8. How does practising NCERT Solutions for Class 9 Maths Chapter 4 improve problem-solving skills?

Regular practice with NCERT Solutions cultivates logical reasoning, enables visualization of algebraic relationships, and strengthens the ability to apply different methods (algebraic and graphical) to solve equations, matching the CBSE exam pattern.

9. Why do students often struggle with the concept of an ‘infinite’ number of solutions in linear equations in two variables?

Students may expect only one or a few solutions, but in two-variable linear equations, every coordinate on the graph line is a solution pair. Understanding this graphical representation, as shown in the NCERT Solutions, clarifies the concept of infinite solutions.

10. What types of mistakes should be avoided when using NCERT Solutions for Class 9 Maths Chapter 4?

  • Avoid plugging in random values without checking if they generate integer or rational solutions required by the question.
  • Always verify that each solution pair (x, y) satisfies the original equation.
  • Do not skip stepwise working – each step in NCERT Solutions matches CBSE marking.

11. How can students ensure full marks in NCERT-based questions for Class 9 Maths Chapter 4?

Follow a thorough, stepwise format as shown in the NCERT Solutions, plot graphs accurately, and support every answer with reasoning and verification, as per CBSE 2025–26 requirements.

12. What is the CBSE-recommended method to verify whether a pair of values solves a given linear equation in two variables?

Substitute the given pair (x, y) in the equation. If both sides of the equation are equal after substitution, then the pair is a solution to the equation as per CBSE standards.

13. How should students approach creating notes for Class 9 Maths Chapter 4 as per NCERT Solutions?

Include definitions, the statement of each method (algebraic and graphical), solved examples, and stepwise approaches explained in the NCERT Solutions to build clear, CBSE-aligned notes.

14. What is the difference between the graphical and algebraic approaches in solving linear equations as per NCERT Solutions?

The algebraic approach involves manipulating values and equations to find solution pairs, while the graphical approach plots those pairs as points to form a straight line, visually representing all possible solutions. NCERT Solutions ensure students can use both techniques confidently for CBSE Class 9 exams.