CBSE Class 9 Linear Equations in Two Variables Sure Shot Questions

Class 9 Mathematics Study Guide: CBSE Class 9 Linear Equations in Two Variables Sure Shot Questions

Review targeted academic resources with the CBSE Class 9 Linear Equations in Two Variables Sure Shot Questions. Built according to official CBSE standards for the 2026-27 term, these downloadable Class 9 Mathematics study materials support effective daily practice and deeper conceptual understanding for Chapter 04 Linear Equations In Two Variables.

Download Chapter 04 Linear Equations In Two Variables Study Material PDF

Navigate directly to the advanced Mathematics study materials using the digital viewer below. Each resource pack includes detailed conceptual summaries and solved practice questions, allowing students to instantly reinforce their learning.

CBSE Class 9 Linear Equations in Two Variables Sure Shot Questions. There are many more useful educational material which the students can download in pdf format and use them for studies. Study material like concept maps, important and sure shot question banks, quick to learn flash cards, flow charts, mind maps, teacher notes, important formulas, past examinations question bank, important concepts taught by teachers. Students can download these useful educational material free and use them to get better marks in examinations.  Also refer to other worksheets for the same chapter and other subjects too. Use them for better understanding of the subjects.

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

2. Find the points where the graph of the equation 3x + 4y = 12 cuts the x-axis and the y-axis.

3. At what point does the graph of the linear equation x + y = 5 meet a line which is parallel to the y-axis, at a distance 2 units from the origin and in the positive direction of x-axis.

4. Determine the point on the graph of the equation 2x + 5y = 20 whose x-coordinate is 5/2 times its ordinate.

5. Draw the graph of the equation represented by the straight line which is parallel to the x-axis and is 4 units above it.

6. Draw the graphs of linear equations y = x and y = – x on the same cartesian plane. What do you observe?

7. Determine the point on the graph of the linear equation 2x + 5y = 19, whose ordinate is 1/1/ 2 times its abscissa.

8. Draw the graph of the equation represented by a straight line which is parallel to the x-axis and at a distance 3 units below it.

9. Draw the graph of the linear equation whose solutions are represented by the points having the sum of the coordinates as 10 units.

10. Write the linear equation such that each point on its graph has an ordinate 3 times its abscissa.

11. If the point (3, 4) lies on the graph of 3y = ax + 7, then find the value of a.

12. How many solution(s) of the equation 2x + 1 = x – 3 are there on the : (i) Number line (ii)Cartesian plane

13. Find the solution of the linear equation x + 2y = 8 which represents a point on (i) x-axis (ii) yaxis

14. For what value of c, the linear equation 2x + cy = 8 has equal values of x and y for its solution.

15. Let y varies directly as x. If y = 12 when x = 4, then write a linear equation. What is the value of y when x = 5?

16. Draw the graph of the linear equation 2x + 3y = 12. At what points, the graph of the equation cuts the x-axis and the y-axis?

17. Show that the points A (1, 2), B (– 1, – 16) and C (0, – 7) lie on the graph of the linear equation y = 9x – 7.

18. The following values of x and y are thought to satisfy a linear equation :

 CBSE Class 9 Linear Equations in Two Variables Sure Shot Questions
Draw the graph, using the values of x, y as given in the above table. At what point the graph of the linear equation (i) cuts the x-axis. (ii) cuts the y-axis.
 
19. The Autorikshaw fare in a city is charged Rs 10 for the first kilometer and @ Rs 4 per kilometer for subsequent distance covered. Write the linear equation to express the above statement. Draw the graph of the linear equation.
 
20. The work done by a body on application of a constant force is the product of the constant force and the distance travelled by the body in the direction of force. Express this in the form of a linear equation in two variables and draw its graph by taking the constant force as 3 units. What is the work done when the distance travelled is 2 units. Verify it by plotting the graph.
 
21. The following values of x and y are thought to satisfy a linear equation, Write the linear equation.
 CBSE Class 9 Linear Equations in Two Variables Sure Shot Questions
 
Draw the graph, using the values of x, y as given in the above table. At what point the graph of the linear equation (i) cuts the x-axis. (ii) cuts the y-axis.
 
22. Draw the graph of the linear equation 3x + 4y = 6. At what points, the graph cuts the x-axis and the y-axis.
 
23. The force exerted to pull a cart is directly proportional to the acceleration produced in the body.
Express the statement as a linear equation of two variables and draw the graph of the same by taking the constant mass equal to 6 kg. Read from the graph, the force required when the acceleration produced is (i) 5 m/sec2, (ii) 6 m/sec2.
 
24. If the temperature of a liquid can be measured in Kelvin units as x°K or in Fahrenheit units as y°F, the relation between the two systems of measurement of temperature is given by the linear equation 9/5 (x- 273) + 32
 
(i) Find the temperature of the liquid in Fahrenheit if the temperature of the liquid is 313°K.
 
(ii) If the temperature is 158° F, then find the temperature in Kelvin.
 
25. The linear equation that converts Fahrenheit (F) to Celsius (C) is given by the relation C = 5F-160/9
 
(i) If the temperature is 86°F, what is the temperature in Celsius?
 
(ii) If the temperature is 35°C, what is the temperature in Fahrenheit?
 
(iii) If the temperature is 0°C what is the temperature in Fahrenheit and if the temperature is 0°F, what is the temperature in Celsius?
 
(iv) What is the numerical value of the temperature which is same in both the scales?
 
26. Draw the graph of x + y = 7 and x – y = 2 on the same graph.
 
27. If the point (3, 4) lies on the graph of the equation 3y = ax + 7, find the value of a.
 
28. The taxi fare in a city is as follows: For the first kilometre, the fare is Rs 8 and for the subsequent distance it is Rs 5 per km. Taking the distance covered as x km and total fare as Rs y, write a linear equation for this information, and draw its graph.
 
29. Solve the equation 2x + 1 = x – 3, and represent the solution(s) on
 
(i) the number line,
 
(ii) the Cartesian plane.
 
30. Give the geometric representations of y = 3 as an equation
(i) in one variable (ii) in two variables
 
31. Give the geometric representations of 2x + 9 = 0 as an equation
(i) in one variable (ii) in two variables
 
32. The force applied on a body is directly proportional to the acceleration produced in the body. Write an equation to express this situation and plot the graph of the equation.
 
33. Draw the graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.
 
34. Draw the graphs of the equations y = x and y = –x in the same graph paper. Find the coordinates of the point where two lines intersect.
 
35. Draw the graphs of the equations 3x – 2y = 4 and x + y – 3 = 0 in the same graph paper. Find the coordinates of the point where two lines intersect.
 
36. Draw the graphs of the equations 3x – 2y + 6 = 0 and x + 2y – 6 = 0 in the same graph paper.
 
Find the area of triangle formed by the two lines and x – axis.
 
37. If the number of hours for which a labourer works is x and y are his wages (in rupees) and y = 2x – 1, draw the graph of work – wages equation. From the graph, find the wages of the labourer if he works for 6 hours.
 
38. A and B are friends. A is elder to B by 5 years. B’s sister C is half the age of B while A’s father D is 8 years older than twice the age of B. If the present age of D is 48 years, find the present ages of A, B and C.
 
39. A three-wheeler scoter charges Rs. 10 for the first km and Rs. 4.50 each for every subsequent km. For a distance of x km, an amount of Rs. Y is paid. Write the linear equation representing the above information.
 CBSE Class 9 Linear Equations in Two Variables Sure Shot Questions
CBSE Class 9 Linear Equations in Two Variables Sure Shot Questions
 
51. The ages of Rahul and Haroon are in the ratio 5:7. Four years later the sum of their ages will be 56 years. What are their present ages?
 
52. Baichung’s father is 26 years younger than Baichung’s grandfather and 29 years older than Baichung. The sum of the ages of all the three is 135 years. What is the age of each one of them?
 
53. Lakshmi is a cashier in a bank. She has currency notes of denominations Rs 100, Rs 50 and Rs 10, respectively. The ratio of the number of these notes is 2:3:5. The total cash with Lakshmi is Rs 4,00,000. How many notes of each denomination does she have?
 
54. I have a total of Rs 300 in coins of denomination Re 1, Rs 2 and Rs 5. The number of Rs 2 coins is 3 times the number of Rs 5 coins. The total number of coins is 160. How many coins of each denomination are with me?
 
55. The organisers of an essay competition decide that a winner in the competition gets a prize of Rs 100 and a participant who does not win gets a prize of Rs 25. The total prize money distributed is Rs 3,000. Find the number of winners, if the total number of participants is 63.
 
56. The digits of a two-digit number differ by 3. If the digits are interchanged, and the resulting number is added to the original number, we get 143. What can be the original number?
 
57. Arjun is twice as old as Shriya. Five years ago his age was three times Shriya’s age. Find their present ages.
 
58. A positive number is 5 times another number. If 21 is added to both the numbers, then one of the new numbers becomes twice the other new number. What are the numbers?
 
59. Sum of the digits of a two-digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the twodigit number?
 
60. One of the two digits of a two digit number is three times the other digit. If you interchange the digits of this two-digit number and add the resulting number to the original number, you get 88. What is the original number?
 
61. Shobo’s mother’s present age is six times Shobo’s present age. Shobo’s age five years from now will be one third of his mother’s present age. What are their present ages?
 
62. There is a narrow rectangular plot, reserved for a school, in Mahuli village. The length and breadth of the plot are in the ratio 11:4. At the rate Rs100 per metre it will cost the village panchayat Rs 75000 to fence the plot. What are the dimensions of the plot?
 
63. A grandfather is ten times older than his granddaughter. He is also 54 years older than her. Find their present ages.
 
64. A man’s age is three times his son’s age. Ten years ago he was five times his son’s age. Find their present ages.
 
65. Present ages of Anu and Raj are in the ratio 4:5. Eight years from now the ratio of their ages will be 5:6. Find their present ages.
 

Please click the link below to download CBSE Class 9 Linear Equations in Two Variables Sure Shot Questions.

Free study material for Mathematics

CBSE Class 9 Mathematics Study Material: Chapter 04 Linear Equations In Two Variables

Essential Notes for Class 9 Mathematics

Explore essential learning tools for Class 9 Mathematics Chapter 04 Linear Equations In Two Variables. This curated collection features in-depth notes and targeted practice questions built around the active 2026 curriculum to streamline your daily revision.

Verified Solutions for Class 9 Mathematics

Built using official NCERT guidelines for Class 9 Mathematics, these materials provide reliable academic support. Integrating past examination questions and step-by-step solutions helps students understand official CBSE grading criteria.

Enhance Accuracy with Online Tests

Maximize your grade potential by utilizing Class 9 Mathematics practice papers in tandem with these structured notes. All printable assignments and interactive mock tests on our platform are updated for the 2026 session and available free of charge.

FAQs

What is included in the advanced study material for Class 9 Mathematics Chapter 04 Linear Equations In Two Variables?

Our advanced study package for Chapter 04 Linear Equations In Two Variables includes detailed concepts, diagrams, Mind Maps, and explanation of complex topics to ensure Class 9 students learn as per syllabus for 2026 exams.

How do Mind Maps for Mathematics Chapter 04 Linear Equations In Two Variables help in revision?

The Mind Maps provided for Chapter 04 Linear Equations In Two Variables act as visual anchors which will help faster recall during high-pressure exams.

Are these Mathematics resources suitable for both classroom teaching and self-study?

Yes, teachers use our Class 9 Mathematics resources for lesson planning as they are in simple language and have lot of solved examples.

Is this advanced study material for Chapter 04 Linear Equations In Two Variables free to download in PDF?

Yes, You can download the complete, mobile-friendly PDF of the Mathematics Chapter 04 Linear Equations In Two Variables advanced resources for free.

Does this material cover rationalized content for the 2026-27 CBSE session?

Yes, our subject matter experts have updated the Chapter 04 Linear Equations In Two Variables material to align with the rationalized NCERT textbooks and have removed deleted topics and added new competency-based questions.