CBSE Class 10 Mathematics Pairs of Linear Equations in Two Variables MCQs

Question: The number of solutions of the pair of linear equations x +3y - 4 = 0 and 2x +6 y = 7 is

a) 0

b) 1

c) 2

d) infinite

Answer: 0

 

Question: The value of k for which the lines (k +1)x +3ky +15 = 0 and 5x + ky +5 = 0 are coincident is

a) 14

b) 2

c) –14

d) –2

Answer: 14

 

Question: The value of g for which the system of equations 5gx -2y =1 and 10x + y = 3 has a unique solution is

a) ≠ – 4

b) =– 4

c) = 4

d) None of these

Answer: ≠ – 4

 

Question: The value of k for which the system of equations 2x + y -3 = 0 and 5x + ky +7= 0 has no solution is

a) 5/2

b) 3/7

c) 2

d) 5

Answer: 5/2

 

Question: If the system of equations 4x + y = 3 and (2k -1) x +(k -1)y = 2k +1 is inconsistent, then k =

a) 3/2

b) -3/2

c) -2/3

d) 2/3

Answer: 3/2

 

Question: The value of k for which the system of equation 2x +3y = 7 and 8x +(k + 4)y -28 = 0 has infinitely many solution is

a) 8

b) 3

c) –3

d) –8

Answer: 8

 

Question: If x = a and y = b is the solution of the equations x - y = 2 and x + y = 4, then the values of a and b are respectively

a) 3 and 1

b) –1 and –3

c) 5 and 3

d) 3 and 5

Answer: 3 and 1

 

Question: A’s age is six times B’s age. Four years hence, the age of A will be four times B’s age. The present ages, in years, of A and B are, respectively

a) 36 and 6

b) 6 and 36

c) 4 and 24

d) 3 and 24

Answer: 36 and 6

 

Question: The sum of the digits of a two digit number is 14. If 18 is added to the number, the digits get reversed. The number is

a) 68

b) 86

c) 59

d) 95

Answer: 68

 

Question: Two numbers are in the ratio 1 : 3. If 5 is added to both the numbers, the ratio becomes 1 : 2. The numbers are

a) 5 and 15

b) 6 and 18

c) 7 and 21

d) 4 and 12

Answer: 5 and 15

 

Question: A pair of linear equations in two variables cannot have

a) exactly two solutions

b) no solution

c) a unique solution

d) infinitely many solutions

Answer: exactly two solutions

 

Question: The pair of equations 3x -2y = 5 and 6x - y = 3 have

a) a unique solution

b) infinitely many solutions

c) no solution

d) two solutions

Answer: a unique solution

 

More Questions.......................................

 

Question. The solutions of the equation 2x–y–5=0 are:

(a) x = 2, y = -1
(b) x = 2, y = 1
(c) x = 1, y = -1
(d) x = -2, y = 1
 

Answer: A

 

Question. The sum of digit of a two digit number is 9. Also, 9 times this number is twice the number

obtained by reversing the order of the digit. The number is:

(a) 20
(b) 16
(c) 18
(d) None of these
 

Answer: C

 

Question. The system of equations kx –y =2 and 6x–2y =3 has a unique solution when:

(a) k = 0
(b) k ≠ 0
(c) k = 3
(d) k ≠ 3
 

Answer: D 

 

Question. A boat can row 1km with stream in 10minutes and 1km against the stream in 20minutes. The speed of the boat in still water is:

(a) 1.5km/hr
(b) 3km/hr
(c) 3.4km/hr
(d) 4.5km/hr
 

Answer: D

 

Question. A boat goes 24km upstream and 28km downstream in 6hours. It goes 30km upstream and 21km downstream in 6hours and 30minutes. The speed of the boat in still water is:

(a) 4km/hr
(b) 6km/hr
(c) 10km/hr
(d) 14km/hr
 

Answer: C

 

Question. Point (4, 3) lies on the line:

(a) 3x + 7y =27
(b) 7x + 2y = 47
(c) 3x +4y = 24
(d) 5x – 4y =1
 

Answer: C

 

Question. The speed of train 150m long is 50km/hr. The time it will take to cross a platform 600m long is:

(a) 50sec
(b) 54sec
(c) 60sec
(d) None of these
 

Answer: B

 

Question. The graph of an equation y = –3 is a line which will be:

(a) parallel to x-axis
(b) parallel to y-axis
(c) passing through origin
(d) on x-axis
 

Answer: A

 

Question. The value of k for which kx + 2y = 5 and 3x + y =1 have unique solution, is:

(a) k = –1
(b) k ≠ 6
(c) k = 6
(d) k =2
 

Answer: B

 

Question. The graph of the equation x–y =0 is:

(a) parallel to x-axis
(b) parallel to y-axis

(c) passing through origin
(d) None of these
 

Answer: C

Question. The solution of the equation 𝑥 + 𝑦 = 5 𝑎𝑛𝑑 𝑥 − 𝑦 = 5 is
a) (0,5)
b) (5,5)
c) (5,0)
d) (10 ,5)

Answer : C

Question. The pair of linear equations 𝑥 = 0 ,𝑥 = − 5 has
a) One solution
b) two solution
c) infinite no: of solution
d) no solution

Answer : D

Question. If 𝑥 = 𝑎,𝑦 = 𝑏 is the solution of the equations 37𝑥 + 43𝑦 = 123 ,43𝑥 + 37𝑦 = 117, then 𝑎³  + 𝑏³ =
a) -7
b) 7
c) 9
d) -9

Answer : B

Question. For what value of ‘k’ do the equations 3𝑥 –𝑦 + 8 = 0 𝑎𝑛𝑑 6𝑥 – 𝑘𝑦 + 16 = 0 represent coincident lines
a) 1/2
b) − (1/2)
c) 2
d) -2

Answer : C

Question. The value of ‘𝑘’ for which the system of equations 4𝑥 + 𝑘𝑦 + 8 = 0 𝑎𝑛𝑑 2𝑥 + 2𝑦 + 2 = 0 has a unique solution is
a) k = 3
b) k ≠ 4
c) k ≠ 0
d) k = 0

Answer : B

Question. The number of solutions of 3𝑥 + 𝑦 = 243 𝑎𝑛𝑑 243𝑥 − 𝑦 = 3 is
a) 0
b) 1
c) 2
d) None

Answer : B

Question. The value of k for which the line 5x + 7y = 3 and 15x + 21y = k coincide is
a) 9
b)5
c) 7
d) 18

Answer : A

Question. 8 chairs and 5 tables cost ₹10500. While 5 chairs & 3 tables cost 6450. Cost of one table
a) 750
b) 900
c) 850
d) 600

Answer : B

Question. Five years hence, father’s age will be three times the age of his daughter. Five years ago, father was seven times as old as his daughter. Their present ages are:

(a) 20 years, 10 years
(b) 40 years, 20 years
(c) 40 years,10 years
(d) 30 years, 10 years
 

Answer: C

 

Question. In a two digit number, the unit’s digit is twice the ten’s digit. If 27 is added to the number, the digits interchange their places. The number is:

(a) 22
(b) 46
(c) 36
(d) 63
 

Answer: C 

 

 

ANSWERS

 

Q13. c Q14. b Q15. c Q16. c Q17. a Q18. a Q19. d Q20. c Q21. d  Q22. c Q23. a Q24. b Q25. a Q26. c Q27. c Q28. d Q29. c  

 

 

Question. For a pair of equation to be consistent and dependent, the pair must have:

(a) no solution
(b) unique solution

(c) infinitely many solution
(d) none of these

 

Answer:  C

 

Question. Graph of every linear equation in two variables represents a _________.

(a) point
(b) straight line
(c) curve
(d) triangle
 

Answer: B

 

Question. Each point on the graph of pair of two lines is a common solution of the lines in case of:

(a) infinitely many solution
(b) only one solution

(c) no solution
(d) none of these
 

Answer: A

Question : The pair of equations y = 0 and y = –7 has
a) one solution
b) two solution
c) infinitely many solutions
d) no solution

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

Question : The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is
a) 3
b) – 3
c) – 12
d) no value

Question : When lines l1 and l2 are coincident, then the graphical solution system of linear equation have
a) infinite number of solutions
b) unique solution
c) no solution
d) one solution

Question : When lines l1 and l2 are parallel, then the graphical solution system of linear equation have
a) infinite number of solutions
b) unique solution
c) no solution
d) one solution

Question : The coordinates of the vertices of triangle formed between the lines and y-axis from the graph is
a) (0, 5), (0, 0) and (6.5,0)
b) (4,2), (0, 0) and (6.5,0)
c) (4,2), (0, 0) and (0,5)
d) none of these

Question : Five years ago Nuri was thrice old as Sonu. Ten years later, Nuri will be twice as old as Sonu. The present age, in years, of Nuri and Sonu are respectively
a) 50 and 20
b) 60 and 30
c) 70 and 40
d) 40 and 10

Question : The pair of equations 5x – 15y = 8 and 3x – 9y = 24/5 has
a) infinite number of solutions
b) unique solution
c) no solution
d) one solution

Question : The pair of equations x + 2y + 5 = 0 and –3x – 6y + 1 = 0 have
a) infinite number of solutions
b) unique solution
c) no solution
d) one solution

Question : The sum of the digits of a two digit number is 9. If 27 is added to it, the digits of the numbers get reversed. The number is
a) 36
b) 72
c) 63
d) 25

Question : Sum of two numbers is 50 and their difference is 10, then the numbers are
a) 30 and 20
b) 24 and 14
c) 12 and 2
d) none of these

Question : The sum of the digits of a two-digit number is 12. The number obtained by interchanging its digit exceeds the given number by 18, then the number is
a) 72
b) 75
c) 57
d) none of these

Question : The sum of a two-digit number and the number obtained by interchanging its digit is 99. If thedigits differ by 3, then the number is
a) 36
b) 33
c) 66
d) none of these

Question : Seven times a two-digit number is equal to four times the number obtained by reversing the orderof its digit. If the difference between the digits is 3, then the number is
a) 36
b) 33
c) 66
d) none of these

Question : A two-digit number is 4 more than 6 times the sum of its digits. If 18 is subtracted from thenumber, the digits are reversed, then the number is
a) 36
b) 46
c) 64
d) none of these

Question : The sum of two numbers is 1000 and the difference between their squares is 25600, then thenumbers are
a) 616 and 384
b) 628 and 372
c) 564 and 436
d) none of these

Question : Five years ago, A was thrice as old as B and ten years later A shall be twice as old as B, then thepresent age of A is
a) 20
b) 50
c) 30
d) none of these

Question : The sum of thrice the first and the second is 142 and four times the first exceeds the second by 138, then the numbers are
a) 40 and 20
b) 40 and 22
c) 12 and 22
d) none of these

Question : The sum of twice the first and thrice the second is 92 and four times the first exceeds seven times the second by 2, then the numbers are
a) 25 and 20
b) 25 and 14
c) 14 and 22
d) none of these

Question : The difference between two numbers is 14 and the difference between their squares is 448, thenthe numbers are
a) 25 and 9
b) 22 and 9
c) 23 and 9
d) none of these

Question : The Solution of tge system of linear equation x/a + y/b = a+b; x/a²  + y/b² = 2 are  
a) x = a and y = b
b) x = a² and y = b² 
c) x = 1 and y = 1
d) none of these

Question : The solution of the system of linear equations 2(ax-by) + (a + 4b) = 0;2(bx + ay) + (b - 4a) = 0 are
a) x = a and y = b
b) x = –1 and y = –1
c) x = 1 and y = 1
d) none of these

Question. The pair of equation x+2y+5=0 and -3x-6y+1=0 have :
(A) A unique solution
(B) Exactly two solutions
(C) Infinitely many solutions
(D) No Solution
Answer : D

Question. The pair of equation y=0 and y=-7 has:
(A) One solution
(B) Two solution
(C) Infinitely many solution
(D) No solution
Answer : D

Question. Aruna has only ₹1 and ₹2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is ₹75, then the number of ₹1 and ₹2 coins are, respectively
(A) 35 and 15
(B) 35 and 20
(C) 15 and 35
(D) 25 and 25
Answer : D

Question. One equation of a pair of dependent linear equations is -5x+7y=2. The second equation can be:
(A) 10x+14y+4=0
(B) -10x-14y+4=0
(C) -10x+14y+4=0
(D) 10x-14y = -4
Answer : D

Question. If a pair of linear equations is consistent, then the lines will be:
(A) Parallel
(B) Always coincident
(C) Intersecting or coincident
(D) Always interesting
Answer : C

Question. If the lines given by 3x+2y=2 and 2x+5y+1=0 are parallel, then the value of k is
(A) −5/4
(B) 2/5
(C) 15/4
(D) 3/2
Answer : C

Question. x and y are 2 different digits. If the sum of the two digit numbers formed by using both the digits is a perfect square, then value of x +y is
(a) 10
(b) 11
(c) 12
(d) 13
Answer : B

Question. The pair of equation x=a and y=b graphically represents lines which are:
(A) Parallel
(B) Intersecting at (b,a)
(C) Coincident
(D) Intersecting at (a,b)
Answer : D

Question. The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages, in years, of the son and the father are, respectively:
(A) 4 and 24
(B) 5 and 30
(C) 6 and 36
(D) 3 and 24
Answer : C

Question. For what value of k, do the equations 3x-y+8=0 and 6x-ky=-16 represents coincident lines?
(A) 1/2
(B) −1/2
(C) 2
(D) -2
Answer : C

CASE STUDY BASED QUESTIONS

CASE STUDY -1
Special offers are short-term pricing strategies that businesses, especially shops will adopt to encourage customers to buy from them. During winter season, a shopkeeper sells a jacket at 8% profit and a sweater at 10 % discount thereby getting a sum of ₹1008. If she had sold the jacket at 10 % profit and the sweater at 8 % discount, she would have got ₹1028. Denoting the cost price of one jacket by ₹ x and the list price of one sweater by ₹ y, answer the following situations.

Question : Represent the first situation algebraically.
a) 12x+10y=11200
b) 10x+12y=11200
c) 12x-10y=11200
d) 10x-12y=1120
Answer : A

Question : Represent the second situation algebraically
a) 46x+55y=51400
b) 55x+46y=51400
c) 55x-46y=51400
d) 46x-55y=51400
Answer : B

Question : The system of linear equations representing both the situations will have.
a) Infinite number of solutions
b) Unique solution
c) No Solutions
d) Exactly two solutions
Answer : B

Question : The graph of the system of linear equations representing both the situations will be
a) Parallel lines
b) Coincident lines
c) Intersecting lines
d) None of these
Answer : C

CASE STUDY 2: 
A pair of linear equations is represented geometrically as shown below.

Question : What can you say about the pair of linear equations?
a) Consistent
b) Inconsistent
c) Dependent
Answer : A

Question : From the graph, find the coordinates of the point, where the line AB intersects the X-axis
a) (5,0)
b) (-2,0)
c) (0,2)
d) (0,0)
Answer : B

Question : From the graph, find the solution of the pair of linear equations
a) (4,2)
b) (2,4)
c) (-2,0)
d) (5,0)
Answer : C

Question : What is the area of the shaded region?
a) 11 sq. units
b) 12 sq. units
c) 13 sq. units
d) 14 sq.units
Answer : D

Question : If a pair of equation is consistent, then the lines will be
a) parallel
b) always coincident
c) always intersecting
d) intersecting or coincident

Question : The solution of the equations x + y = 14 and x – y =4 is
a) x = 9 and y = 5
b) x = 5 and y = 9
c) x = 7 and y = 7
d) x = 10 and y = 4

Question : The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by b3, the fraction becomes ½ , then the fraction
a) 4/7
b) 5/7
c) 6/7 
d) 3/7

Question : The value of k for which the system of equations x – 2y = 3 and 3x + ky = 1 has a uniquesolution is
a) k = – 6
b) k ≠ – 6
c) k = 0
d) no value

Question : If a pair of equation is inconsistent, then the lines will be
a) parallel
b) always coincident
c) always intersecting
d) intersecting or coincident

Question : The value of k for which the system of equations 2x + 3y = 5 and 4x + ky = 10 has infinite many solution is
a) k = – 3
b) k ≠ – 3
c) k = 0
d) none of these

Question : The value of k for which the system of equations kx – y = 2 and 6x – 2y = 3 has a unique solution is
a) k = – 3
b) k ≠ – 3
c) k = 0
d) k ≠ 0

Question : Sum of two numbers is 35 and their difference is 13, then the numbers are
a) 24 and 12
b) 24 and 11
c) 12 and 11
d) none of these

Question : The solution of the equations 0.4x + 0.3y = 1.7 and 0.7x – 0.2y = 0.8 is
a) x = 1 and y = 2
b) x = 2 and y = 3
c) x = 3 and y = 4
d) x = 5 and y = 4

Question : The solution of the equations x + 2y = 1.5 and 2x + y = 1.5 is
a) x = 1 and y = 1
b) x = 1.5 and y = 1.5
c) x = 0.5 and y = 0.5
d) none of these

Question : The value of k for which the system of equations x + 2y = 3 and 5x + ky + 7 = 0 has no solution is
a) 10
b) 6
c) 3
d) 1

Question : The value of k for which the system of equations 3x + 5y = 0 and kx + 10y = 0 has a non-zero solution is
a) 0
b) 2
c) 6
d) 8