CBSE

LINEAR EQUATIONS IN TWO VARIABLES 9 WS 2

Class 09 - Mathematics

Section A
1. Assertion (A): A linear equation 2x + 3y = 5 has a unique solution. [1]
Reason (R): A linear equation in two variables has infinitely many solutions.

a) Both A and R are true and R is the correct b) Both A and R are true but R is not the
explanation of A. correct explanation of A.

c) A is true but R is false. d) A is false but R is true.

2. Assertion (A): The point (1, 1) is the solution of x + y = 2. [1]
Reason (R): Every point which satisfy the linear equation is a solution of the equation.

a) Both A and R are true and R is the correct b) Both A and R are true but R is not the
explanation of A. correct explanation of A.

c) A is true but R is false. d) A is false but R is true.

3. Assertion (A): The point (0, 3) lies on the graph of the linear equation 3x + 4y = 12. [1]
Reason (R): (0, 3) satisfies the equation 3x + 4y = 12.

a) Both A and R are true and R is the correct b) Both A and R are true but R is not the
explanation of A. correct explanation of A.

c) A is true but R is false. d) A is false but R is true.

4. Assertion (A): The graph of the linear equation x - 2y = 1 passes through the point (3, 1). [1]
Reason (R): Every point lying on graph is not a solution of x - 2y = 1.

a) Both A and R are true and R is the correct b) Both A and R are true but R is not the
explanation of A. correct explanation of A.

c) A is true but R is false. d) A is false but R is true.

5. Assertion (A): For all values of k, ( , k) is a solution of the linear equation 2x + 3 = 0. [1]
−3

Reason (R): The linear equation ax + b = 0 can be expressed as a linear equation in two variables as ax + y + b
= 0.

a) Both A and R are true and R is the correct b) Both A and R are true but R is not the
explanation of A. correct explanation of A.

c) A is true but R is false. d) A is false but R is true.

6. State True or False: [1]
(a) The two solutions of the linear equation x + 2y = 1 is (1, 0) and(3, -1). [1]
7. Fill in the blanks: [1]
(a) If πx + 3y = 25 and y = 1, then the value of x will be ________. [1]
8. Which one of the options is true, and why? y = 3x + 5 has [1]

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 a) only two solutions b) infinitely many solutions

c) a unique solution d) No solution

9. Write two solutions for equation: x + πy = 4 [1]
–
10. Check wheather ( √3, 0) is the solution of the equation 2x - y = 6 or not. [1]
11. Check whether (0, 5) is solution of the equation 5x - 4y = 20 [1]
12. If x = 0 and y = k is a solution of the equation 5x - 3y = 0, find the value of k. [1]
13. Show that x = 3 and y = 2 is a solution of the linear equation 2x + 3y = 12 [1]
14. Find two solutions for equation: 4x + 3y = 12 [1]
15. Check whether (2, -2) is the solution of the equation 2x - y = 6 or not. [1]
– –
16. Find whether ( √2, 3√2 ) is a solution of x - 3y = 9 or not. [1]
17. If πx + 3y = 25 and y = 1, then find x. [1]
Section B
18. Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y = k. [2]
19. Match the following: [2]
(a) 37x − 39y = 150, 39x − 37y = 154 (i) (2,-1)
(b) 149x − 330y = − 511, − 330x + 149y = −32 (ii) (3,-1)

(c) 47x + 31y = 63, 31x + 47y = 15 (iii) (0,0)

(d) The graph of 4x + 5y = 0 is passing through (iv) (1,2)
20. Write two solutions of the equation 4x - 5y = 15. [2]
21. Write two solutions of the form x = 0, y = a and x = b, y = 0 : -4x + 3y = 12 [2]
22. Find the value of the following equation for x = l, y = l as a solution. 3x + ay = 6 [2]
23. Find whether (0, 2) is the solution of the equation x – 2y = 4 or not? [2]
24. Find four solutions for the following equation :2(x – 1) + 3y = 4 [2]
25. Solve the equation for x: 5(4x + 3) = 3(x - 2) [2]
26. Find whether the given equation have x = 2, y = 1 as a solution: [2]
2x + 3y = 7
27. Solve the given equation for x: , where x ≠ 0, x ≠ 1,x ≠ -1 [2]
3 1 4
+ =
x−1 x+1 x

28. How many solution(s) of the equation 3x + 2 = 2x - 3 are there on the : [2]
i. Number line?
ii. Cartesian plane?
– –
29. Find whether (√2, 4√2) is the solution of the equation x – 2y = 4 or not? [2]
30. Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3y =k. [2]
31. Find whether the given equation have x = 2, y = 1 as a solution: [2]
x+y+4=0
32. Find whether(4, 0) is the solution of the equation x – 2y = 4 or not? [2]
33. Find whether the given equation have x = 2, y = 1 as a solution: [2]
2x – 3y = 1
34. If x = 3k + 2 and y = 2k - 1 is a solution of the equation 4x - 3y + 1 = 0, find the value of k. [2]
35. Write four solutions of the equation: πx + y = 9 [2]
36. Find whether (2, 0) is the solution of the equation x – 2y = 4 or not? [2]
37. Find four solutions for the following equation : x = 0 [2]

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38. Check whether (2, ) is solutions of the equation 5x - 4y = 20 [2]
−5

39. Find whether the given equation have x = 2, y = 1 as a solution: [2]

2x – 3y + 7 = 8
40. Write four solutions of the equation: x = 4y. [2]
41. Find whether the given equation have x = 2, y = 1 as a solution: [2]
5x + 3y = 14
42. Write four solutions of the equation: 2x + y = 7 [2]
43. Solve the following equation for x: (5x + 1)(x + 3) - 8 = 5(x + 1)(x + 2) [2]
44. Find four solutions for the following equation : x – y = 0 [2]
45. Find whether the given equation have x = 2, y = 1 as a solution:x + y + 4 = 0. [2]
46. Find whether (1, 1) is the solution of the equation x – 2y = 4 or not? [2]
47. Find whether the given equation have x = 2, y = 1 as a solution: [2]
2x + 5y = 9
48. Find four solutions for the following equation: x + y = 0 [2]
Section C
49. Find four solutions for the following equation: 12x + 5y = 0 [3]
50. Find four solutions for the following equation :12x + 5y = 0 [3]
51. Find at least 3 solutions for the linear equation 2x – 3y + 7 = 0. [3]
52. Find at least 3 solutions for the following linear equation in two variables: [3]
2x + 5y = 13
53. Find solutions of the form x = a, y = 0 and x = 0, y = b for the following pairs of equations. Do they have any [3]
common such solution for equations 9x + 7y = 63 and x + y = 10
54. For what value of c, the linear equation 2x + cy = 8 has equal values of x and y for its solution? [3]
55. Find at least 3 solutions for the following linear equation in two variables: [3]
2x + 3y = 4
56. Find at least 3 solutions for the following linear equation in two variables: 2x – 3y + 7 = 0 [3]
57. Find solutions of the form x = a, y = 0 and x = 0, y = b for the following pairs of equations. Do they have any [3]
common such solution?
3x + 2y = 6 and 5x + 2y = 10
58. Find solutions of the form x = a, y = 0 and x = 0, y = b for the following pairs of equations. Do they have any [3]
common such solution?
5x + 3y = 15 and 5x + 2y = 10
59. Find the solution of the linear equation x + 2y = 8 which represents a point on [3]
i. The x-axis
ii. The y-axis
60. Find at least 3 solutions for the following linear equation in two variables: 5x + 3y = 4. [3]
61. Find at least 3 solutions for the following linear equation in two variables: x + y – 4 = 0 [3]
Section D
Question No. 62 to 65 are based on the given text. Read the text carefully and answer the questions: [4]
Ajay lives in Delhi, The city of Ajay's father in laws residence is at Jaipur is 600 km from Delhi. Ajay used to travel
this 600 km partly by train and partly by car.
He used to buy cheap items from Delhi and sale at Jaipur and also buying cheap items from Jaipur and sale at Delhi.

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Once From Delhi to Jaipur in forward journey he covered 2x km by train and the rest y km by taxi.
But, while returning he did not get a reservation from Jaipur in the train. So first 2y km he had to travel by taxi and the
rest x km by Train. From Delhi to Jaipur he took 8 hrs but in returning it took 10 hrs.

62. Write the above information in terms of equation.

63. Find the value of x and y?
64. Find the speed of Taxi?
65. Find the speed of Train?
Question No. 66 to 69 are based on the given text. Read the text carefully and answer the questions: [4]
Ajay is writing a test which consists of ‘True’ or ‘False’ questions. One mark is awarded for every correct answer while
¼ mark is deducted for every wrong answer. Ajay knew answers to some of the questions. Rest of the questions he
attempted by guessing.

66. If he answered 110 questions and got 80 marks and answer to all questions, he attempted by guessing were wrong, then
how many questions did he answer correctly?
67. If he answered 110 questions and got 80 marks and answer to all questions, he attempted by guessing were wrong, then
how many questions did he guess?
68. If answer to all questions he attempted by guessing were wrong and answered 80 correctly, then how many marks he
got?
69. If answer to all questions he attempted by guessing were wrong, then how many questions answered correctly to score
95 marks?
Question No. 70 to 73 are based on the given text. Read the text carefully and answer the questions: [4]
Peter, Kevin James, Reeta and Veena were students of Class 9th B at Govt Sr Sec School, Sector 5, Gurgaon.
Once the teacher told Peter to think a number x and to Kevin to think another number y so that the difference of
the numbers is 10 (x > y).
Now the teacher asked James to add double of Peter's number and that three times of Kevin's number, the total was
found 120.
Reeta just entered in the class, she did not know any number.
The teacher said Reeta to form the 1st equation with two variables x and y.
Now Veena just entered the class so the teacher told her to form 2nd equation with two variables x and y.

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Now teacher Told Reeta to find the values of x and y. Peter and kelvin were told to verify the numbers x and y.

70. What are the equation formed by Reeta and Veena?

71. What was the equation formed by Veena?
72. Which number did Peter think?
73. Which number did Kelvin think?
Section E
74. Find five different solutions of the equation: 3y = 4x [5]
4(x+1)
75. Solve for x:
3x+2
+ =
2
(2x + 1) [5]
7 5 3

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