MCQ Questions for Class 10 Maths Pair of Linear Equations in Two Variables

The stepping stone of a student’s career is when they appear for their first board exam and Mathematics is a key subject. Chapter 3 Pair of Linear Equations in Two Variables requires a lot of practice and concentration. These Multiple-Choice Questions will help students to secure better in the CBSE exams. The MCQs are framed according to the latest CBSE syllabus and exam pattern. Chapter 3 Pair of Linear Equations in Two Variables MCQs assist students to check whether their learning and concepts of the chapter are clear and on which areas they have to work more. Practicing these MCQs will ensure that students become more proficient at tackling different types of questions.

Class 10 Maths Pair of Linear Equations in Two Variables MCQs

1. Graphically, the pair of equations 7x – y = 5; 21x – 3y = 10 represents two lines which are

A. intersecting at one point
B. parallel
C. intersecting at two points
D. coincident

Answer: B

2. The pair of equations 3x – 5y = 7 and – 6x + 10y = 7 have

A. a unique solution
B. infinitely many solutions
C. no solution
D. two solutions

Answer: C

3. If a pair of linear equations is consistent, then the lines will be

A. always coincident
B. parallel
C. always intersecting
D. intersecting or coincident

Answer: D

4. The pair of equations x = 0 and x = 5 has

A. no solution
B. unique/one solution
C. two solutions
D. infinitely many solutions

Answer: C

5. The pair of equation x = – 4 and y = – 5 graphically represents lines which are

A. intersecting at (- 5, – 4)
B. intersecting at (- 4, – 5)
C. intersecting at (5, 4)
D. intersecting at (4, 5)

Answer: B

6. One equation of a pair of dependent linear equations is 2x + 5y = 3. The second equation will be

A. 2x + 5y = 6
B. 3x + 5y = 3
C. -10x – 25y + 15 = 0
D. 10x + 25y = 15

Answer: C

7. The graph of x = -2 is a line parallel to the

A. x-axis
B. y-axis
C. both x- and y-axis
D. none of these

Answer: B

8. If in the equation x + 2y = 10, the value of y is 6, then the value of x will be

A. -2
B. 2
C. 4
D. 5

Answer: A

9. The pair of equations 3x – 5y = 7 and – 6x + 10y = 7 have

A. a unique solution
B. infinitely many solutions
C. no solution
D. two solutions

Answer: C

10. The pair of equations x = 0 and x = 5 has

A. no solution
B. unique/one solution
C. two solutions
D. infinitely many solutions

Answer: C

11. If in the equation x + 2y = 10, the value of y is 6, then the value of x will be

A. -2
B. 2
C. 4
D. 5

Answer: A

12. The graph of the equation 2x + 3y = 5 is a

A. vertical line
B. straight line
C. horizontal line
D. none of these

Answer: B

13. The pair of equations x + 2y – 5 = 0 and −3x – 6y + 15 = 0 have:

A. A unique solution
B. Exactly two solutions
C. Infinitely many solutions
D. No solution

Answer: C

14. If the lines given by
3x + 2ky = 2
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

15. One equation of a pair of dependent linear equations is –5x + 7y – 2 = 0. 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

16. Two numbers are in the ratio 5 : 6. If 8 is subtracted from each of the numbers, the ratio becomes 4 : 5. Then the numbers are:

A. 40, 42
B. 42, 48
C. 40, 48
D. 44, 50

Answer: C

17. One equation of a pair of dependent linear equation 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

18. A pair of linear equations which has a unique solution x = 2, y = -3 is

A. x + y = -1
2x – 3y = -5
B. 2x + 5y = -11
4x + 10y = -22
C. 2x – y = 1
3x + 2y = 0
D. x – 4y – 14 = 0
5x – y – 13 = 0

Answer: D

19. If x = a, y = b is the solution of the equation x – y = 2 and x + y = 4, then the value of a and b are respectively

A. 3 and 5
B. 5 and 3
C. 3 and 1
D. -1 and -3

Answer: C

20. 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 of the son and the father, in years, are respectively

A. 4 and 24
B. 5 and 30
C. 6 and 36
D. 3 and 24

Answer: C

21. Graphically, the pair of equations 6x – 3y + 10 = 0
2x – y + 9 = 0
represents two lines which are

A. Intersecting at exactly one point
B. Intersecting at two points
C. Coincident
D. Parallel

Answer: D

22. If a pair of linear equations is consistent, then
the lines will be

A. parallel
B. always coincident
C. intersecting or coincident
D. always intersecting

Answer: C

23. The pair of equations 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

24. 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

Answer: D