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

Question. The value of k for which the system of linear equations 3x + y = 1, (2k –1)x + (k –1)y = 2k + 1 have no solution is
(a) k = 2
(b) k = 4
(c) k = 6
(d) k = 8 

Answer: A

Question. If 4/x +3y =8; 6/x -4y =-5 , then
(a) x = 2, y = 2
(b) x = 1, y = –1
(c) x = 2, y = –2
(d) x = 3, y = – 3

Answer: A

Question. The value of k for which the following pair of linear equations have infinitely many solutions: 2x + 3y = 7, (k – 1)x + (k + 2)y = 3k is
(a) 2
(b) 4
(c) 7
(d) 9

Answer: C

Question. The value of k for which the system of equations kx + 4y = k – 4, 16x + ky = k have infinite number of solutions is
(a) k = 2
(b) k = 4
(c) k = 6
(d) k = 8

Answer: D

Question. The value of k for which the system of linear equations x + 2y = 3, 5x + ky + 7 = 0 is inconsistent is
(a) −14/ 3
(b) 2/ 5
(c) 5
(d) 10

Answer: D

Question. The value of m for which the pair of linear equations 2x + 3y – 7 = 0 and (m – 1) x + (m + 1) y = (3m – 1) has infinitely many solutions is
(a) 5
(b) 8
(c) – 5
(d) 8

Answer: A

Question. The pair of linear equations 3x/2 + 5y/3 and 9x + 10y = 14 is
(a) consistent
(b) inconsistent
(c) consistent with one solution
(d) consistent with many solutions

Answer: B

Question. What type of a system of equations is the pair of linear equations 2x - 3y = 8 and 4x - 6y = 9?
(a) Consistent system
(b) Inconsistent system
(c) Dependent system
(d) Independent system

Answer: B

Question. Find the values of 'x' and y, for the equations a²/x - b²/y = 0 , a²b/x + b²a/y = a + b where x, y ≠ 0 .
(a) x = a² , y = b²
(b) x = b² , x = a²
(c) x = b/a , y = a/b
(d) x = 1/b , y = 1/a

Answer: A

Question. Solution of the simultaneous linear equations: 2x/y − y/2 = − 1/6 and x/2 + 2y/3 = 3 is
(a) x = 2, y = – 3
(b) x = – 2, y = 3
(c) x = 2, y = 3
(d) x = – 2, y = – 3

Answer: C

Question. If 4/x + 5y = 7; 3/x + 4y = 5 , then
(a) x = 1 3 , y = –1
(b) x = 8, y = 3
(c) x = 4, y = 7
(d) x = 5, y = 9

Answer: A

Question. If 1/2x − 1/y = –1 and 1/x +1/ 2y = 8, (x ≠ 0, y ≠ 0), then
(a) x = 1/ 4 , y = 1/ 2
(b) x = 1/ 3 , y = 1/ 5
(c) x = 1/ 6 , y = 1/ 8
(d) x = 1/ 6 , y = 1/ 4

Answer: D

Question. If 2/x + 2y = 15 and 2/x − 4y = 3, then the values of x and y, respectively are
(a) 2/ 11 , 2
(b) 3, 1/ 3 
(c) 4, 1/ 4 
(d) 1/ 4 , 4

Answer: A

Question. On comparing a₁/ a2 , b₁/ b₂ , c₁/ c₂ , the graphical representation of equations 2x – 3y = 8 and 4x – 6y – 9 = 0 will
(a) Intersecting lines
(b) Coincident lines
(c) Parallel lines
(d) None of the options

Answer: C

Question. The coordinates of vertices of a triangle formed by the equations x – y + 1 = 0, 3x + 2y – 12 = 0 and x-axis are
(a) (1, 3), (–2, 3), (3, 0)
(b) (3, 4), (–3, 5), (2, 3)
(c) (2, 5), (–3, 0), (5, 0)
(d) (2, 3), (–1, 0), (4,0)

Answer: D

Question. The lines represented by the equations 5x – 4y + 8 = 0, 7x + 6y – 9 will
(a) intersect at a point
(b) be parallel
(c) be coincident
(d) None of the options

Answer: A

Question. If the pair of equations x sin θ + y cos θ = 1 and x + y = √2 has infinitely many solutions, then the value of θ is
(a) 30°
(b) 45°
(c) 60°
(d) 90°

Answer: B

Question. For what value of p, the following pair of linear equations have infinitely many solutions? (p – 3)x + 3y = p, px + py = 12
(a) 4
(b) 6
(c) 9
(d) 11

Answer: B

Question. The value(s) of k for which the pair of linear equations kx + y = k² and x + ky = 1 have infinitely many solutions is
(a) 1
(b) 2
(c) 3
(d) 4

Answer: A

Question. When 3x + 2y = 11 3 and –7x + 5y = 313 are solved by elimination method, we get
(a) x = 5 /19 , y =111/ 37
(b) x = 9 /85 , y = 160/ 27
(c) x = −4/ 71 , y = 5/ 28
(d) x = y −7/ 87 ,Y = 170/87 

Answer: D

Question. Solving 3x – 5y – 4 = 0 and 9x = 2y + 7 by the elimination method, we get the values of x and y as
(a) x = 9 /13 , y = −5/ 13
(b) x = 11/24 , y = 15/ 23
(c) x =17 / 25 , y =16 / 9
(d) None of the options

Answer: A

Question. The value of k for which the system of linear equations 3x + y = 1, (2k –1)x + (k –1)y = 2k + 1 have no solution is
(a) k = 2
(b) k = 4
(c) k = 6
(d) k = 8

Answer: A

Question. The value of k for which the system of linear equations x + 2y = 3, 5x + ky + 7 = 0 is inconsistent is
(a) −14/ 3
(b) 2/ 5
(c) 5
(d) 10

Answer: D

Question. If 4/x + 3y = 8 ; 6/x − 4y = −5 , then
(a) x = 2, y = 2
(b) x = 1, y = –1
(c) x = 2, y = –2
(d) x = 3, y = – 3

Answer: A

Question. If x/2 + y = 0.8 ; 7/x + y/2 = 10 then
(a) x = 2, y = 0.5
(b) x = 0.4, y = 0.6
(c) x = 0.3, y = 3
(d) x = 0.5, y = 0.8

Answer: B

Question. The difference between two numbers is 26 and the larger number exceeds thrice of the smaller number by 4. The numbers are
(a) 39, 13
(b) 12, 38
(c) 37, 11
(d) None of the options

Answer: C

Question. 1/ 3x + y + 1/ 3x - y = 3/ 4 and 1/ 2(3x +y) −1/2(3x − y) = −1/ 8 , where 3x + y ≠ 0, 3x – y ≠ 0, then
(a) 1, 2
(b) 1, 1
(c) 1, 3
(d) 1, 4

Answer: B

Question. If the equations kx – 2y = 3 and 3x + y = 5 represent two intersecting lines at unique point, then the value of k is
(a) Only 4
(b) Only 5
(c) Only 6
(d) Any number other than –6

Answer: D

Question. If 3 – (x – 5) = y + 2, 2(x + y) = 4 – 3y, then
(a) x = 13/ 4 , y = 9 /10
(b) x = 7/ 16 , y = 5 /8
(c) x = 4/ 9 , y = 9/ 12
(d) x = 26/ 3 , y = −8/ 3

Answer: D

Question. For what value of p, the following pair of linear equations have infinitely many solutions?
(p – 3)x + 3y = p, px + py = 12
(a) 4
(b) 6
(c) 9
(d) 11

Answer: B

Question. For which values of k, the pair of equations kx + 3y = k – 3 and 12x + ky = k have no solution?
(a) k = 2
(b) k = 6
(c) – 6
(d) k = –2

Answer: C

Question. If 2x + y = 23 and 4x – y = 19, then the value of (5y – 2x) and (y/x - 2) respectively are
(a) 31, −5/ 7
(b) 28, 3 /11
(c) 24, 5/ 8
(d) 10, 17/ 21

Answer: A

Question. If 2x = 5y + 4, 3x – 2y + 16 = 0, then
(a) x = 2, y = –2
(b) x = 3, y = –3
(c) x = 4, y = 5
(d) x = – 8, y = – 4

Answer: D

Question. If 2/x + 3/y = 13 and 5/x − 4/y = –2, then x + y equals
(a) 1/ 6
(b) −1/ 6
(c) 5/ 6
(d) −5/ 6

Answer: C

Question. A purse contains 25 paise and 10 paise coins. The total amount in the purse is ` 8.25. If the number of 25 paise coins is one-third of the number of 10 paise coins in the purse, then the total number of coins in the purse is
(a) 60
(b) 40
(c) 80
(d) 72

Answer: A

Question. For what values of p, the pair of equations 4x + py +8 =0 and 2x +2y +2 = 0 have unique solution?
(a) p = 4
(b) p ≠ 4
(c) p = 7
(d) p ≠ 7

Answer: B

Question. What type of straight lines will be represented by the system of equations 2x + 3y = 5 and 4x + 6y = 7?
(a) Intersecting
(b) Parallel
(c) Conincident
(d) None of the options

Answer: B

Question. For what value of k, the pair of linear equations 3x + y = 3 and 6x + ky = 8 does not have a solution?
(a) 2
(b) –2
(c) 4
(d) –4

Answer: A

Question. For what values of p, the pair of equations 4x + py +8 =0 and 2x +2y +2 = 0 have unique solution?
(a) p = 4
(b) p ≠ 4
(c) p = 7
(d) p ≠ 7

Answer: B

Question. The value of x and y for the following system of equations, respectively are
21/x + 47/y = 110
47/x + 21/y = 162 ⇒ x, y ≠ 0
(a) x = 1 2 , y = –1
(b) x = 1 3 , y = 1
(c) x = 1 4 , y = 2
(d) x = 1 3 , y = 1 4

Answer: B

Question. If x + 2y – 3 = 0, 3x – 2y + 7 = 0, then
(a) x = –1, y = 2
(b) x = 1, y = 2
(c) x = 2, y = 3
(d) x = – 2, y = – 3

Answer: A

Question. Given: 10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz. The pair of linear equations representing the above situation and their solution, respectively are
(a) x + y = 10, x – y = –4; (3, 7)
(b) x – y = 10, x + y = 4; (3, 5)
(c) 2x + y = 10, 2x – y = 4; (2, 5)
(d) 2x – y = 10, 2x + y = 4

Answer: A

Question. Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. The dimensions of the garden are (use graphical method)
(a) Length = 20 m, width = 16 m
(b) Length = 16 m, width = 24 m
(c) Length = 18 m, width = 12 m
(d) Length = 24 m, width = 15 m

Answer: A

Question. The solution of the system of equations x + y = 5, x – y = 2 using substitution method is:
(a) x = 7/ 2 , y = 3/ 2
(b) x = 3 /5 , y = 1/ 2
(c) x = 3 /5 , y = 1 /4
(d) x = 2 /5 , y = 5/ 2

Answer: A

Question. If the equations kx – 2y = 3 and 3x + y = 5 represent two intersecting lines at unique point, then the value of k is
(a) Only 4
(b) Only 5
(c) Only 6
(d) Any number other than –6

Answer: D

Question. If 7(y + 3) – 2(x + 2) = 14, 4(y – 2) + 3(x – 3) = 2, then
(a) x = 1, y = 4
(b) x = 3, y = 5
(c) x = 5, y = 1
(d) None of the options

Answer: C

Question. The sum of a two-digit number and the number obtained by interchanging the digits is 132. If the two digits differ by 2, the number is
(a) 45
(b) 75
(c) 85
(d) 115

Answer: B

Question. Which of the following is not a solution of the pair of equations 3x – 2y = 4 and 6x – 4y = 8?
(a) x = 2, y = 1
(b) x = 4, y = 4
(c) x = 6, y = 7
(d) x = 5, y = 3

Answer: D

Question. If x + 2y – 3 = 0, 3x – 2y + 7 = 0, then
(a) x = –1, y = 2
(b) x = 1, y = 2
(c) x = 2, y = 3
(d) x = – 2, y = – 3

Answer: D

Question. The value of k so that the following system of equations has no solution is
3x – y – 5 = 0, 6x – 2y + k = 0 
(a) 10
(b) –10
(c) Both 10 and –10
(d) All real values of k except –10

Answer: D

Question. If the pair of equations x + y = 5 and 2x + 2y = 10 is consistent, the two solutions obtained graphically are
(a) (0, 4), (4, 0)
(b) (7, –2), (2, 7)
(c) (0, 5), (5, 0)
(d) None of the options

Answer: C

Question. If 2x = 5y + 4, 3x – 2y + 16 = 0, then
(a) x = 2, y = –2
(b) x = 3, y = –3
(c) x = 4, y = 5
(d) x = – 8, y = – 4

Answer: D

Question. The solution of given system of equations:
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. When the following pair of equations is solved by reducing them to a pair of linear equations, we get 1/x − 4 /y = 2 and 1/x + 3/ y = 9
(a) x = 1/ 6 , y = 1
(b) x = 1, y = 1/ 5
(c) x = 1/ 3 , y = 5
(d) x = 1/ 4 , y = 1/ 3

Answer: A

Question. The coordinates of the vertices of a triangle formed by the equations of sides are: y = x; y = 2x; x + y = 6 are
(a) (0, 0), (3, 3), (2, 4)
(b) (0, 1), (5, 5), (2, 5)
(c) (4, 4), (3, 0), (1, 6)
(d) None of the options

Answer: A

Question. If 6(ax + by) = 3a + 2b; 6(bx – ay) = 3b – 2a, then
(a) x = 1/ 2 , y = 1/ 2
(b) x = – 1/ 2 , y = – 1/ 2 
(c) x = 1/ 2 , y = 1/ 3
(d) x = – 1/ 2 , y = – 1/ 3

Answer: C

Question. A boat travels for 7 hours. If it travels 4 hours downstream and 3 hours upstream, then it covers the distance of 116 km. But if it travels 3 hours downstream and 4 hours upstream, it covers the distance of 108 km. The speed of the boat is
(a) 16 km/h
(b) 22 km/h
(c) 18 km/h
(d) None of the options

Answer: A

Assertion and Reason:
(a) If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
(b) If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
(c) If Assertion is correct but Reason is incorrect.
(d) If Assertion is incorrect but Reason is correct.

Question. Assertion : x + y – 4 = 0 and 2x + ky – 3 = 0 has no solution if k = 2
Reason : a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 are consistent if a₁/a₂ ≠ b₁/b₂

Answer: B

Question. Assertion : If the system of equations 2x + 3y = 7 and 2ax + (a + b) y = 28 has infinitely many solutions, then 2a – b = 0
Reason : The system of equations 3x – 5y = 9 and 6x – 10y = 8 has a unique solution.

Answer: C

Question. Assertion : If the pair of lines are coincident, then we say that pair of lines is consistent and it has a unique solution.
Reason : If the pair of lines are parallel, then the pair has no solution and is called inconsistent pair of equations.

Answer: D