## Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables MCQs

**Class 10 Maths MCQs for Chapter 3 (Pair of Linear Equations in Two Variables)** are provided here online with answers. These multiple-choice questions will help students to score good marks in the board exam. These objective questions are prepared as per the latest CBSE syllabus and NCERT textbook. The MCQs for Class 10 Maths Chapter 3 are prepared by our subject experts as per the latest exam pattern.

## Class 10 Maths MCQs for Pair of Linear Equations in Two Variables

Class 10 Maths exam datasheet is been released by the CBSE board. It is time for students to revise the chapters for the board exam. Students are required to solve these questions here and choose the appropriate answer for them

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

1. A pair of linear equations a_{1}x + b_{1}y + c_{1} = 0; a_{2}x + b_{2}y + c_{2} = 0 is said to be inconsistent, if

2. Graphically, the pair of equations 7x â€“ y = 5; 21x â€“ 3y = 10 represents two lines which are

(a) intersecting at one point

(b) parallel

(c) intersecting at two points

(d) coincident

3. The pair of equations 3x â€“ 5y = 7 and â€“ 6x + 10y = 7 have

(a) a unique solution

(b) infinitely many solutions

(c) no solution

(d) two solutions

4. 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

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

(a) no solution

(b) unique/one solution

(c) two solutions

(d) infinitely many solutions

6. The pair of equation x = â€“ 4 and y = â€“ 5 graphically represents lines which are

(a) intersecting at (- 5, â€“ 4)

(b) intersecting at (- 4, â€“ 5)

(c) intersecting at (5, 4)

(d) intersecting at (4, 5)**Answer**

7. For what value of k, do the equations 2x â€“ 3y + 10 = 0 and 3x + ky + 15 = 0 represent coincident lines

8. If the lines given by 2x + ky = 1 and 3x â€“ 5y = 7 are parallel, then the value of k is

**Answer**

9. 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 â€“ 25y + 15 = 0

(d) 10x + 25y = 15**Answer**

10. If x = a, y = b is the solution of the equations x + y = 5 and 2x â€“ 3y = 4, then the values of a and b are respectively

(a) 6, -1

(b) 2, 3

(c) 1, 4

(d) 19/5, 6/5**Answer**

11. 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

12. The graph of y = 4x is a line

(a) parallel to x-axis

(b) parallel to y-axis

(c) perpendicular to y-axis

(d) passing through the origin

13. The graph of y = 5 is a line parallel to the

(a) x-axis

(b) y-axis

(c) both axis

(d) none of these

14. Two equations in two variables taken together are called

(a) linear equations

(b) quadratic equations

(c) simultaneous equations

(d) none of these

15. If am bl then the system of equations ax + by = c, lx + my = n, has

(a) a unique solution

(b) no solution

(c) infinitely many solutions

(d) none of these

16. 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

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

(a) vertical line

(b) straight line

(c) horizontal line

(d) none of these

18. The value of k, for which equations 3x + 5y = 0 and kx + lOy = 0 has a non-zero solution is

(a) 6

(b) 0

(c) 2

(d) 5

19. The value of k, for which the system of equations x + (k + l)y = 5 and (k + l)x + 9y = 8k â€“ 1 has infinitely many solutions is

(a) 2

(b) 3

(c) 4

(d) 5

20. The value of k for which the equations (3k + l)x + 3y = 2; (k2 + l)x + (k â€“ 2)y = 5 has no solution, then k is equal to

(a) 2

(b) 3

(c) 1

(d) -1

21. 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)

22. Asha has only â‚¹1 and â‚¹2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is â‚¹75, then the number of â‚¹1 and â‚¹2 coins are, respectively

(a) 35 and 15

(b) 15 and 35

(c) 35 and 20

(d) 25 and 25

23. The fatherâ€™s age is six times his sonâ€™s age. Four years hence, the age of the father will be four times his sonâ€™s age. The present ages of the son and the father are, respectively

(a) 4 and 24

(b) 5 and 30

(c) 6 and 36

(d) 3 and 24

24. The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is

(a) 27

(b) 72

(c) 45

(d) 36

25. **The pairs of equations x+2y-5 = 0 and -4x-8y+20=0 have:**

(a) Unique solution

(b) Exactly two solutions

(c) Infinitely many solutions

(d) No solution

26.

**. If a pair of linear equations is consistent, then the lines are:**

(a) Parallel

(b) Always coincident

(c) Always intersecting

(d) Intersecting or coincident

27. **The pairs of equations 9x + 3y + 12 = 0 and 18x + 6y + 26 = 0 have**

(a) Unique solution

(b) Exactly two solutions

(c) Infinitely many solutions

(d) No solution

28. **If the lines 3x+2ky â€“ 2 = 0 and 2x+5y+1 = 0 are parallel, then what is the value of k?**

(a) 4/15

(b) 15/4

(c) â…˜

(d) 5/4

29. **If one equation of a pair of dependent linear equations is -3x+5y-2=0. The second equation will be:**

(a) -6x+10y-4=0

(b) 6x-10y-4=0

(c) 6x+10y-4=0

(d) -6x+10y+4=0

30. **The solution of the equations x-y=2 and x+y=4 is:**

(a) 3 and 1

(b) 4 and 3

(c) 5 and 1

(d) -1 and -3

31. **A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. The fraction obtained is:**

(a) 3/12

(b) 4/12

(c) 5/12

(d) 7/12

** 32. The solution of 4/x+3y=14 and 3/x-4y=23 is:**

(a) â…• and -2

(b) â…“ and Â½

(c) 3 and Â½

(d) 2 and â…“

33. ** Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Her speed of rowing in still water and the speed of the current is:**

(a) 6km/hr and 3km/hr

(b) 7km/hr and 4km/hr

(c) 6km/hr and 4km/hr

(d) 10km/hr and 6km/hr

34. **The angles of cyclic quadrilaterals ABCD are: A = (6x+10), B=(5x)Â°, C = (x+y)Â° and D=(3y-10)Â°. The value of x and y is:**

(a) x=20Â° and y = 10Â°

(b) x=20Â° and y = 30Â°

(c) x=44Â° and y=15Â°

(d) x=15Â° and y=15Â°

35. **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)

36. **The pair of equations 5x â€“ 15y = 8 and 3x â€“ 9y = 24/5 has**

(a) one solution

(b) two solutions

(c) infinitely many solutions

(d) no solution

37. **The pair of equations x + 2y + 5 = 0 and â€“3x â€“ 6y + 1 = 0 have**

(a) a unique solution

(b) exactly two solutions

(c) infinitely many solutions

(d) no solution

38. **The value of c for which the pair of equations cx â€“ y = 2 and 6x â€“ 2y = 3 will have infinitely many solutions is**

(a) 3

(b) -3

(c) -12

(d) no value

**39. If the lines representing the pair of linear equations a _{1}x + b_{1}y + c_{1} = 0 and a_{2}x + b_{2}y + c_{2} = 0 are coincident, then**

(a) a_{1}/a_{2} = b_{1}/b_{2}

(b) a_{1}/a_{2} = b_{1}/b_{2} = c_{1}/c_{2}

(c) a_{1}/a_{2} â‰ b_{1}/b_{2}

(d) a_{1}/a_{2} = b_{1}/b_{2} â‰ c_{1}/c_{2}

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

(a) x + y = -1; 2x â€“ 3y = -5

(b) 2x + 5y = -11; 4x + 10y = -22

(c) 2x â€“ y = 1; 3x + 2y = 0

(d) x â€“ 4y â€“ 14 = 0; 5x â€“ y â€“ 13 = 0

41. **The fatherâ€™s age is six times his sonâ€™s age. Four years hence, the age of the father will be four times his sonâ€™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

**42. If the pair of linear equations has a unique solution, then the lines representing these equations will **

(a) coincide

(b) intersect at one point

(c) parallel to each other

(d) parallel to x-axis

43. **Which of the following method(s) is/are used to find the solution of a pair of linear equations algebraically?**

(a) Substitution Method

(b) Elimination Method

(c) Cross- multiplication Method

(d) All the above

44. **The graphical representation of a pair of equations 4x + 3y â€“ 1 = 5 and 12x + 9y = 15 will be**

(a) parallel lines

(b) coincident lines

(c) intersecting lines

(d) perpendicular lines

45. 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

46. The pair of equations y = 0 and y = -7 has

(Ð°) one solution

(b) two solutions

(c) infinitely many solutions

(d) no solution

47. For what value of k, for the equations 3x â€“ y + 8 = 0 and 6x â€“ ky = -16 represents coincident lines?

(a) 12

(b) â€“12

(c) 2

(d) -2

48. The value of c for which the pair of equations cx â€“ y = 2 and 6x â€“ 2y = 3 will have infinitely many solutions is

(a) 3

(b) -3

(c) -12

(d) no value

49. 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 â€“ 14y + 4 = 0

(c) -10x + 14y + 4 = 0

(d) 10x â€“ 14y = -4

50. If x = a, y = b is the solution of the equation x â€“ 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

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