CBSE Class 9 Mathematics Linear Equations in two variables Assignment Set B

1 How many line(s) pass through the point (0, 0)?
(A) Only one
(B) Two
(C) Infinitely many
(D) Three
Answer : C

2 Which of t he following is t rue about y = 4x- 3?
(A) It has a unique solution.
(B) It has only two solut ions.
(C) It has infinitely many solutions.
(D) It is a linear equation in one variable.
Answer : D

3 If x = - 2 and y = 3 is the solution of the equation 3x - 5y = k, find 'k'.
(A) - 21
(B) - 9
(C) - 18
(D) 19
Answer : A

4 What does an equation of the form ax + by + c = 0, where a and b are nonzero numbers represent?
(A) A straight line
(B) A circle
(C) A triangle
(D) A quadrilateral
Answer : A

5 Which of the following is the equation of a line parallel to y-axis?
(A) y = -2
(B) y = 0
(C) y = 5
(D) X = -4
Answer : D

6 What is the equation of X-axis?
(A) x = 0
(B) x = -2
(C) y = 0
(D) y = - 2
Answer : C

7 For which condition does the equation px + qy + r = 0 represent a linear equation in two variables?
(A) p ≠ 0,q = 0
(B) q ≠ 0,q = 0
(C) p = 0,q = 0
(D) p ≠ 0,q ≠ 0
Answer : D

8 Which of the following is correct with respect to the line x + 1 = 0?
(A) It is parallel toy-axis.
(B) It passes through (0, - 1 ).
(C) It is parallel to x-axis.
(D) It passes through (0, 0).
Answer : A

9 Which is the equation of a line passing through the origin?
(A) y = 2
(B) X = 4
(C) y = 5x
(D) x = -7
Answer : C

10 Identify t he correct stat ement from the following with respect to the line y - 2 = 0.
(A) It is parallel to X-axis.
(B) It is parallel toY-axis.
(C) It passes through the origin.
(D) It passes through x = 2 .
Answer : A

11 If (3, 4) is a solution of the equation 5x - 2y = k, find the value of k.
(A) 7
(B) 6
(C) 5
(D) 4
Answer : A

12 If t he point (2,-3) lies on the graph of the equation ay = 7x- 26, what is the value of'a'?
(A) 37
(B) 16
(C) -5
(D) 4
Answer : D

13 The cost of a shirt of a particular brand is ₹ 800. What is the linear equation when the cost of x number of shirts is ₹ y?
(A) X = 800y
(B) X = 800 + y
(C) y = 800x
(D) y = 800 + x
Answer : C

14 Where does the point of the form (p, p) ∀ p ≠ 0 always lie?
(A) x - axis
(B) origin
(C) on the line y = x
(D) on the line x + y = 0
Answer : C

15 What is the solution set of 5/3 - 2/x = 8/x for x ≠ 0?
(A) {2}
(B) (18/5)
(C) (26/5)
(D) {6}
Answer : D

16 What is the solution set of √k+64-8 = -2?
(A) {-28}
(B) {-124}
(C) {4}
(D) { }
Answer : A

17 What are all the roots for the equation 3lw- 14l - 6 = 21?
(A) 19
(B) 23
(C) 5 and 23
(D) 9 and 19
Answer : C

18 What is the solution of the equation given in the box?
3y + 4 / 2 , 2y - 5 / 3  = 31/2
(A) y = 1
(B) y = 6
(C) y = 7
(D) y = 13
Answer : C

19 Veena heard that it is 82° Fahrenheit in Ooty. She knows that F = 9/5 C + 32, where F represents the temperature in degrees Fahrenheit and C represents the temperature in degrees Celsius. Which is closest to the temperature in Ootyl in degrees Celsius?
(A) 28
(B) 63
(C) 90
(D) 180
Answer : A

20 Identify the point at which the graph of the equation 7x - 9y - 21 = 0 cuts x- axis.
(A) (21 I 0)
(B) (0, 9)
(C) (31 0)
(D) (3 1 1)
Answer : C

21 Which of the following equations represents a straight line passing through the points (1, 6), (0, 4) and (-2, 0)?
(A) 2x - y = - 4
(B) x - 2y = - 4
(C) 2x + y = 4
(D) x + 2y = - 4
Answer : A

22 Identify the equation of line parallel to y -axis and 5-units away from the origin.
(A) y = 5
(B) X = -5
(C) X = 5
(D) y = -5
Answer : C

23 Find the point at which the straight lines represented by linear equations x- y = 2 and 3x - 2y = 7 intersect.
(A) (1 1 1)
(B) (1 1 3)
(C) (21 2)
(D) (3, 1)
Answer : D

24 Which of the following is true?
(A) The equation of the x-axis is y = 0.
(B) The graph of every linear equation in two variable is a curve.
(C) y = 3x + 5 has a unique solution.
(D) The graph of the equation 2y- 5 = 0 is parallel toy - axis.
Answer : A

25 If the point (2p, p - 3) lies on the graph of the equation 3x + 2y + 12 = 0, find the value of p.
(A) -3/4
(B) -1/6
(C) 7/15
(D) 6/7
Answer : A

26 If the expressions y - 1 0 and 24 - y are equal, what is the value of y?
(A) 34
(B) 14
(C) 17
(D) 12
Answer : C

27 How many kilograms of tea at ₹ 50 per kg should be mixed with 35 kg of tea costing ₹ 60 per kg so as to sell the mixture at ₹ 57 per kg without gaining or losing anything in the transaction?
(A) 5 kg
(B) 7 kg
(C) 25 kg
(D) 15 kg
Answer : D

28 Vihan spent ₹ 132 to buy movie tickets for 20 children and 4 adults. Adult tickets cost ₹ 3 more than child tickets. If A is the price of an adult ticket and S is the price of a child ticket, which system of equations could be used to find the price of each adult and child ticket?

Answer : B

29 The graph of a system of linear equations is given.

Based upon the graph, which is the apparent sol ution to the sy stem of equations?
(A) (2, 5)
(B) (3, 4)
(C) (4, 3)
(D) (5, 2)
Answer : B

30 Find'x'if x - 2 / x + 3 = x + 2 / x - 3, x ≠ 3, x ≠ - 3
(A) 3
(B) 0
(C) 1
(D) - 2
Answer : C

31 Three consecutive numbers such that twice the first, 3 times the second and 4 times the third together make 191. Find the least of the consecutive numbers.
(A) 18
(B) 21
(C) 19
(D) 20
Answer : B

32 Rishab rode his bike to a store 5 km from his house. The table given shows the distance from the store paired wi th the number of minutes after leav ing his house

Which of following equations of line best fits for the given data?
(A) y = - 0.2x + 43
(B) y = - 02x + 6.1
(C) y = - 0.3x + 4.9
(D) y = - 03x + 6.1
Answer : D

33 A man is five times as old as his son. After 2 years the man will be four times as old as his son. What is the present age of the man?
(A) 35 years
(B) 30 years
(C) 6 years
(D) 31 years
Answer : C

34 Mega city High School earned ₹ 5100 on tickets sales for a play. The cost per ticket was ₹ 12. If trepresents the number of tickets sold to the play, which of the following equations could be used to determine the number of tickets sold for the play?
(A) 12 =5 100t
(B) 12t =5100
(C) t =5100 - 12
(D) t = 5100.12
Answer : B

35 The function f(x) = 35 + 15x represents the amount of money, in Rupees, Mr. Ramesh earns for working x hours. How much money does Mr. Ramesh earn for working 25 hours?
(A) ₹ 75
(B) ₹ 375
(C) ₹ 410
(D) ₹ 1250
Answer : C

36 Two planes start from a city and fly in opposite directions, one averaging a speed of 40 km/hour greater than the second. If they are 3400 km apart from 5 hours, find the sum of their average speeds.
(A) 680 km/h
(B) 360 km/h
(C) 320 km/h
(D) 640 km/h
Answer : A

37 Which equation represents the relationship between time, t, and distance, d?

Answer : B

38 The angles of a pentagon are in the ratio 2 : 3 : 3 : 3 : 4. Find the least angle of the pentagon.
(A) 108°
(B) 72°
(C) 27°
(D) 90°
Answer : B

39 Straight lines represented by linear equations x + y = 2 and Sx - 3y = 2 intersect at which of the given points?
(A) (1,2)
(B) (1, 1)
(C) (2, 1)
(D) (3,2)
Answer : B

40 A woman sells to the first customer half her stock and half an apple, to the second
customer she sells half her remaining stock and half an apple, and so on to the third, and to a fourth customer. She finds that she has now 15 apples left. How many apples did she have before she started selling?
(A) 63
(B) 127
(C) 240
(D) 289
Answer : D

41 A student was asked to divide a number by 17/8. Instead, he act ually mult iplied it by 17/8 and hence got 225 more t han the expected answer. What was the expected answer?
(A) 126
(B) 136
(C) 64
(D) 84
Answer : C

42 If a and b are real numbers, when does the equation 3x - 5 + a = bx + 1 has a unique solution x?
(A) for all a and b
(B) no root
(C) if a ≠ 6
(D) if b ≠ 3
Answer : D

43 In a class, 3/5 of the students are girls and rest are boys. If 2/9 of the girls and 1/4 of the boys are absent, what part of the total number of students are present?
(A) 23/30
(B) 23/36
(C) 18/49
(D) 17/25
Answer : A

44 How many solutions does a linear equation in two variable have?
(A) 1
(B) Infinite
(C) 2
(D) 0
Answer : B

45 The course of an enemy submarine as plotted on a set of rectangular axes is 2x + 3y = 5. On the same axes the course of the destroyer is indicated by x - y = 10. What is t he point (x, y) at which the submarine can be destroyed?
(A) (- 7, 3)
(B) (-3, 7)
(C) (3, - 7)
(D) (7,-3)
Answer : D

46 When a ball bounces, it rises to 3/4 of the height from which it fell. If t he ba ll is dropped from a height of 32 m, how high will it rise at the third bounce?
(A) 14(1/2)m
(B) 13(1/2)m
(C) 13m
(D) 14
Answer : B

Topic: Linear Equation In Two Variables

Q1: Find the value of K if x=2 and y=1 is a solution of the equation (k-2)x + 4y = 10 and have the graph of the equation. Write the co-ordinate of the point where the graph cuts the y-axis.

Q2: Express y in terms of x in the equation 2x-3y = 12. Find the points where the line represented by this equation cuts x-axis and y- axis.

Q3: Draw the graph of two lines whose equations are 3x-2y -6 =0 and x+2y-6=0 on the same graph paper. Find the area of triangle formed by the two lines and x-axis.

Q4: Find the solutions of the form x=a, y=0 and x=0, y=b for the following equations:

2x+5y = 10 and 2x+3y = 6. Is there any common solution?

Q5: If the points A(3,5) and B(1,4) lie on the graph of the line ax+by = 7, find the values of a and b.

Q6: Draw the graphs of 2x+ y=6 and 2x-y +2 =0. Shade the region bounded by these lines and x-axis. Find the area of the shaded region.

Q7: Draw the graphs of x- y=1 and 2x+y =8. Shade the region bounded by these lines and y-axis. Shade the area bounded by these two lines and y-axis. Also, determine this area.

Q8: Ravish tells his daughter Aarushi, “Seven years ago, I was seven times as old as you will be”. If present ages of Aarushi and Ravish are x and y respectively, represent this situation algebraically as well as graphically.

Q9: If the points A(3,5) and B(1,4) lie on the graph of the line ax+ by = 7, find the values of a and b.

Q10: Draw the graphs of each of the following linear equations in Cartesian plane

(i) x-2=0

(ii) 2x + 4 = 3x + 1

Please click the link below to download CBSE Class 9 Mathematics Linear Equations in two variables Assignment Set B