CBSE Class 10 Mathematics Pair of Linear Equations in Two Variables Worksheet Set F

Question. If seven books and 5 pens cost Rs 410, whereas five books and seven pens cost Rs.334 then the cost ofthree books and four pens would be
a) Rs.135
b) Rs.145
c) Rs.255
d) Rs.198

Answer: D

Question. The pair of equations x = 2 and y = 3 graphically represents the lines which are
a) Coincident
b) intersecting at (2, 3)
c) parallel
d) intersecting at (3, 2)

Answer: B

Question. The pair of equations x + 3y = 12 and 2x + 6y - 24 = 0 represents:
a) Consistent system with unique solution
b) Consistent system with infinite solution
c) Inconsistentsystem with unique solution
d) Inconsistent system with no solution

Answer: B

Question. The pair of linear equations which has unique solution as x = 3 and y = - 1 is
a) x – y = 4 and 2x –y = 6
b) x + y = 2 and 2x + 3y = 3
c) x - 2y = 5 and 2x + 3y = 9
d) x + 2y = 1 and 2x + y = 7

Answer: B

Question. For what value of k, 2x + 3y = 4, (k + 2) x + 6y = 3k + 2 will have infinitely many solutions.
a) 1
b) 4
c) 5
d) 2

Answer: D

Question. Two numbers are in the ratio 5:6. If 8 is subtracted from each of the numbers, the ratio becomes 4:5. Find the numbers
a) 45, 54
b) 40,48
c) 55,66
d) 50,60

Answer: B

Question. Given the linear equation 4x + 6y − 9 = 0, another linear equation in two variables such that the geometrical representation of the pair(s), so formed will be consistent is:
(i) 2x + 3y – 9 = 0 (ii) 5x - 6y – 9 = 0 (iii) 8x + 12y - 18 = 0 (iv) 12x + 18y - 18 = 0
a) Only (ii) and (iii)
b) None of the above
c) All the of options
d) Only (i) and (iv)

Answer: A

Question. Solve 2𝑥 + 3𝑦 = 11 and 2𝑥 − 4𝑦 = − 24 and hence find the value of ‘m’ for such that 𝑦 = mx +  3.
a) - 1
b) 1
c) 0
d) - 2

Answer: A

Question. The pair of equations 5𝑥 − 15𝑦 = 8 and 3𝑥 − 9𝑦 = 24 has
a) One solution
b) two solutions
c) infinitely many solutions
d) no solution

Answer: D

Question. If 2x - 3y = 7 and (a + b)x - (a + b - 3)y = 4a + b have infinite solution, then value of (a, b) is
a) ( - 3,1)
b) ( - 5, - 1)
c) (5,1)
d) (3, - 1)

Answer: B

Question. The sides of a rectangle are 19 units,10 units, 2x - y and - x + 2y units as shown in the figure given below then the values of x, y and x + y are:

a) 16,13,29
b) 13,16,29
c) 10,19,29
d) 19,10,29

Answer: A

Question. The cost of an article A is 10 % more than the cost of article B if their total cost is ₹441 then cost of article A and B are
a) ₹210, ₹231
b) ₹231, ₹210
c) ₹ 221, ₹220
d) ₹220, ₹ 221

Answer: B

Question. What type of straight lines will be represented by the system of equations 2x + 3y = 5 and 4x + 6y = 7?
a) Always intersecting
b) parallel
c) coincident
d) coincident or intersecting

Answer: B

Question. Difference of the areas of two squares is 144 m2. If the difference of their perimeters is 32 m, then the sides of the two squares is:
a) 12m and 13 m
b) 13 m and 5 m
c) 13m and 8 m
d) 12 m and 8 m

Answer: B

Question. If a pair of linear equations is consistent, then the graph of the lines will be
a) Parallel
b) intersecting
c) intersecting or coincident
d) always coincident

Answer: C

Question. If the lines given by x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the value of k is:
a) −5/4
b) −2/5
c) 5/4
d) 5

Answer: C

Question. The solution for the given system 𝑥 + 𝑦 = 𝑎 + 𝑏, 𝑎x − 𝑏y = 𝑎² − 𝑏² is
a) 𝑥 = 2𝑎, 𝑦 = 𝑏
b) 𝑥 = 𝑎, 𝑦 = 2𝑏
c) 𝑥 = 𝑎, 𝑦 = 𝑏
d) 𝑥 = 1/𝑎 , 𝑦 = 1/𝑏

Answer: C

Question. The area of triangle formed by the line 𝑥/𝑎 + 𝑦/𝑏 = 1 with the coordinate axes is
a) 2ab
b) ab
c) (1/4)ab
d) (1/2)ab

Answer: D

Question. Sharat has ₹2 and ₹5 coins with him.If total number of coins are 16 and the amount of money is ₹ 50, Then the number of ₹2 and ₹5 coins are
a) 8 and 8
b) 6 and 10
c) 10 and 6
d) 15 and 4

Answer: C

Question. The pair of linear equations 𝑦 = 2 𝑎𝑎𝑎𝑎𝑎𝑎 𝑦 = −3 has
a) Only one common solution
b) no common solution
c) many common solutions
d) none of the options

Answer: B

Question. Which of the following pairs of linear equations are consistent?
a) x – y = 8, 3x – 3y = 16
b) x + y = 5, 2x + 2y = 15
c) 2x + y – 6 = 0, 4x – 2y – 4 = 0
d) 2x – 2y – 2 = 0, 4x – 4y – 5 = 0

Answer: C

Question. The solution of the pair of linear equations x + 3y = 6 and 2x – 3y = 12 representedgraphically is

a) (6, 0)
b) (0, 0)
c) (0, 2)
d) (0, - 4)

Answer: B

(CASE STUDY BASED QUESTIONS)

1. Arav planned a surprise for his grandparents, he and his family consisting of his father, mother and his sister aged 10 years, planned to take his grandfather and grandmother who were above 60 years to an amusement park. Arav who is 2 years older than his sister insisted on enjoying family rides while his sister wanted to go for kids rides in the amusement park.The cost of ticket and the cost of rides are given in table 1 and 2 respectively:

Question. If x adults and y children went to park on Wednesday and they paid Rs 4985 for the tickets, the linear equation would be:
a) 1025𝑥 + 925𝑦 = 4985
b) 500𝑥 + 600𝑦 = 4985
c) 815x + 635y = 4985
d) 635𝑥 + 925𝑦 = 4985

Answer: C

Question. Cost of kids ride is half the cost of family ride then the equation would be
a) z - 2p = 0
b) p = 2z
c) z + 2p = 0
d) z = p

Answer: A

Question. If Arav and his sister took kids ride and remaining 4 members took family rides and they paid ₹500,the equation representing the situation is:
a) 4p + 2z = 500
b) 2z = 4p + 500
c) z - 2p = 500
d) 4z + 2p = 500

Answer: D

Question. If all 6 of them had taken up family rides then they would have paid ₹600 then what is the cost of a family ride for each member
a) ₹200
b) ₹100
c) ₹50
d) cannot say

Answer: B

Question. If the speed of family ride is 10 more than twice the speed of kids ride, the equation would be:
(taking speed of family ride as 𝑥𝑥 m/sec and kids ride as y m/sec)
a) 𝑥 = 10 + 2𝑦
b) 𝑦 = 10 + 2𝑥
c) 𝑥 + 𝑦 = 12
d) 4𝑦 − 4𝑥 = 12

Answer: A

2. Rahul is studying in X Standard. He is making a kite to fly it on a Sunday. Few questions came to his mind while making the kite. Give answers to his questions by looking at the figure. The length of the sides are AB = 20 cm, BC = X + Y,CD = 35 CM,AD = X + 2Y

Question. Based on the information given above which of the following pair of equations are correct:
a) 𝑥 + 𝑦 = 20 and 𝑥 + 2𝑦 = 35
b) 𝑥 + 𝑦 = 35 and 𝑥 + 2𝑦 = 20
c) 𝑥 = 𝑦 + 20 and 2𝑦 = 35 + 𝑥
d) 𝑥 = 35 + 𝑦 and 2𝑦 = 20 + 𝑥

Answer: A

Question. On solving the equations the value of y would be
a) 20
b) 15
c) 10
d) 5

Answer: B

Question. On drawing the graph of equation 𝑥 + 𝑦𝑦 = 20 which of the points given below will not lie on it
a) ( - 4,24)
b) (0, - 20)
c) (20,0)
d) (10,10)

Answer: B

Question. The graph of linear equation 𝑥 + 𝑦 = 20 will intercept y axis at
a) ( - 4,24)
b) (0, - 20)
c) (20,0)
d) (0,20)

Answer: D

Question. The area of triangle formed by the line 𝑥 + 𝑦 = 20 with x and y axis would be
a) Approximately 200 sq units
b) Exactly 200 square units
c) Less than 200 square units
d) More than 200 sq units

Answer: B

3. Ramani and her friend Rita are doing their post - graduation and they have to stay in a hostel away from their home. At the hostel , part of monthly hostel charges are fixed and the remaining depends on the mess charge. When Ramani takes food for 22 days from mess, she has to pay ₹ 2000 as hostel charges whereas Rita, who takes food for 30 days, from mess pays ₹ 2400 as hostel charges.

Question. Taking fixed monthly hostel charges as x and mess charge to be y per day the equation algebraically representing the amount paid by Ramani would be
a) 𝑥 + 22𝑦 = 2000
b) 𝑥 + 22𝑦 = 2400
c) 𝑥 + 30𝑦 = 2000
d) 𝑥 + 30𝑦 = 2400

Answer: A

Question. Taking fixed monthly hostel charges as x and mess charge to be y per day the equation algebraically representing the amount paid by Rita would be
a) 𝑥 + 22𝑦 = 2000
b) 𝑥 + 22𝑦 = 2400
c) 𝑥 + 30𝑦 = 2000
d) 𝑥 + 30𝑦 = 2400

Answer: D

Question. The amount of fixed monthly hostel charge to be paid is:
a) ₹800
b) ₹700
c) ₹900
d) ₹65

Answer: C

Question. The fees one has to pay towards mess charges  if they take food at the hostel for 12 days would be
a) ₹600
b) ₹1200
c) ₹900
d) ₹1000

Answer: A

Question. The equation 2𝑥 + 𝑦 = 100 has:
a) infinite solutions
b) only one solution
c) (5, 95) is a solution of the equation
d) (100, 0) is a solution of the equation

Answer: A

4. Places A and B are 56km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 4 hours. If they travel towards each other, they meet in one hour.

Question. Taking the speed of car at A is x km/hr and that of car at B is y km/h. The equation that would represent the situation algebraically (assume y > x) when the cars are travelling in opposite direction
a) 𝑥 + 𝑦 = 56
b) 𝑥 − 𝑦 = 56
c) 𝑥y = 56
d) 𝑦 − 𝑥 = 56

Answer: A

Question. Taking the speed of car at A is x km/hr and that of car at B is y km/hr.The equation that would represent the situation algebraically (assume y>x) when the cars are travelling in samedirection
a) 4𝑥 + 4𝑦 = 56
b) 4𝑥 − 4𝑦 = 56
c) 𝑥 + 𝑦 = 56
d) 4𝑦 − 4𝑥 = 56

Answer: D

Question. The speed of car at A is:
a) 21 km/h
b) 35 km/h
c) 56 km/h
d) 15 km/h

Answer: A

Question. The( speed of car A + Speed of car B) is:
a) 21 km/h
b) 35 km/h
c) 56 km/h
d) 25 km/h

Answer: C

Question. The graph of the equations obtained in (i) and (ii) would intersect at
a) (21, 35)
b) (35, 21)
c) (55, 35)
d) (35,55)

Answer: B

5. The members of housing colony of fortune avenue took up the task of planting saplings in the parks located in their venture it was informed that there are two possibilities
Case 1: 4 men and 6 boys can finish a piece of work in 5 days
Case 2: 3 men and 4 boys can finish it in 7 days.

Question. Assuming that a man can complete the work alone in x days, his work in four days would be:
a) 1/𝑥
b) x
c) 4/𝑥
d) 4x

Answer: C

Question. If a man alone takes x days to complete the work while a boy takes y days to complete the work. The
equation representing case 1 is given by:
a) 4/𝑥 + 6/𝑦 = 5
b) 6/𝑥 + 4/𝑦 = 1/5
c) 6/𝑥 + 4/𝑦 = 5
d) 4/𝑥 + 6/𝑦 = 1/5

Answer: D

Question. As per the case study, In how many days can a man alone complete the work.
a) 35 days
b) 70 days
c) 50 days
d) 100 days

Answer: A

Question. For the equation 3/𝑥 + 4/𝑦 = 1/7 if 1/𝑥 is taken as a and 1/𝑦 is taken as b the equation would reduce to
a) 4b + 3a = 1
b) 3a + 4b = 1
c) 21a + 28 b = 1
d) 21 b + 28 a = 7

Answer: C

Question. Identify among the following which is a solution of the equation 3/𝑥 + 4/𝑦 = 1/7
a) (24,56)
b) (42,24)
c) (42,56)
d) (24,24)

Answer: C

6. Two students were playing with number cards one of the student observed that the sum of the two - digit number he picked up and the number obtained by reversing the digits is 66. The digits of the number were found to differ by 2.He asked his friend to answer the questions given below based on the clues he had given about the number. His friend took the digit in tens place as x and the digit in ones place to be y, also he was told that 𝑥 > 𝑦

Question. The sum digits would be represented by the equation
a) x + y = 6
b) x + 6 = y
c) y + 6 + x = 0
d) xy = 6

Answer: A

Question. If 10 x + y is the original number what would be the reversed number
a) 𝑥/10 + 𝑦
b) 1y + 10 x
c) x + 10y
d) x + 𝑦/10

Answer: C

Question. The difference between the digits of the two digit number is two , the student wrote the following equations :
(I) x – y = 2 (II) y – x = 2 (III) x = 2 + y (IV) y = 2 + x
Which of the following are true?
a) All the above equations are correct
b) None of the equations above are correct
c) Only equations (I) and (III) are correct
d) only equations (II) and (IV) are correct

Answer: C

Question. The original number on the number card picked by the student is
a) 24
b) 42
c) 44
d) 22

Answer: B

Question. The sum of original and twice the reversed number is:
a) 66
b) 132
c) 90
d) 75

Answer: C

7. A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km down - stream. Determine the speed of the stream and that of the boat in still water. Assuming the speed of boat to be x km/h and that of stream to be y km/h

Answer the questions below

Question. The net speed of boat (in km/h) during upstream would be
a) x – y
b) x + y
c) 𝑥/𝑦
d) xy

Answer: A

Question. Which of the following statement is true?
a) Speed of boat is 3 km/h
b) Speed of stream is 8 km/h
c) Speed of boat is 8 km/h
d) Speed of boat + stream is 10km/h

Answer: C

Question. The graph of the equation 40u + 55v = 13 would be
a) Linear
b) parabola
c) line parallel to x axis
d) line passing through origin

Answer: A

Question. If the system of linear equations kx + 2y = 5 and 3x + y = 1 has a unique solution then
a) 𝑘 ≠ 3/2
b) 𝑘 = 6
c) 𝑘 ≠ 6
d) 𝑘 ≠ 2/3

Answer: C

8. A student was observing Railway tracks at secunderabad railway station, these tracks represent a pair of linear equations as shown below, based on the observation answer the questions given:

Question. The equation 3x + 2y = 6 intersects x axis at
a) (0,3)
b) (3,0)
c) (2,0)
d) (0,2)

Answer: C

Question. If ( - 3,4) is a solution of the system of linear equations 8x + ay = 8
a) 10
b) 8
c) 2
d) 11

Answer: A

Question. The equation of first track is 3x + 2y = 12, if this is found to intersect another track at certain point which of the following cannot be the equation of the other track
a) 4y + 6x = 24
b) 2x + 4y = 24
c) 12x + 8y = 12
d) 9x + 8y = 48

Answer: C

Question. The vertices of the triangle formed by the equation 3x + 2y = 12 with the x and y axis:
a) (0,0) (0,4)(6,0)
b) (0,0) (0,6) (4,0)
c) (0,0) (2,0)(0,3)
d) (0,0) (3,0)(0,2)

Answer: B