## MCQ Questions for Class 10 Maths: Ch 3 Pair of Linear Equations in Two Variables 1. 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
► (c) no solution

2. If A : Homogeneous system of linear equations is always consistent. R : x = 0, y = 0 is always a solution of the homogeneous system of equations with unknowns x and y, then which of the following statement is true?
(a) A is true and R is the correct explanation of A
(b) A is false and R is not a correrct explanation of A
(c) A is true and R is false
(d) A is false and R is true
► (a) A is true and R is the correct explanation of A

3. How many solutions of the equation 15x – 14y + 11 = 0 are possible?
(a) 2
(b) No solution
(c) 1
(d) Infinite
► (d) Infinite

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
► (c) two solutions

5. Which of following is not a solution of 3a + b = 12?​
(a) (3, 3)
(b) (5, -3)
(c) (4, 0)
(d) (2, 4)
► (d) (2, 4)

6. he pair of linear equations 2kx + 5y = 7, 6x – 5y = 11 has a unique solution if –
(a) k = -3
(b) k = 3
(c) k = 5
(d) k = -5
► (a) k = -3

7. 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
► (d) intersecting or coincident

8. If x = a, y = b is the solution of the equations x + y = 5 and 2x – 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
► (d) 19/5,  6/5

9. The pair of equations 3x + 4y = k, 9x + 12y = 6 has infinitely many solutions if –
(a) k = 2
(b) k = 6
(c) k = 6
(d) k = 3
► (a) k = 2

10. Find the solution to the following system of linear equations:
2p+3q = 9 p – q = 2​
(a) (4,2)
(b) (3,1)
(c) (2,-3)
(d) (-4,1)
► (b) (3,1)

11. Find the value of ‘a” for which the system of equations ax + 2y – 4 = 0 and x – y – 3 = 0 will represent intersecting lines?​
(a) a ≠ -2
(b) a = -2
(c) a = 2
(d) a ≠ 2
► (a) a ≠ -2

12. Which of the following pair of linear equations is inconsistent?​
(a) 2x + 3y = 7; 4x + 6y = 5
(b) x – 2y = 6; 2x + 3y = 4
(c) 9x – 8y = 17; 18x -16y = 34
(d) 5x – 3y =11; 7x + 2y =13
► (a) 2x + 3y = 7; 4x + 6y = 5

13. If the pair of equation has no solution, then the pair of equation is :
(a) inconsistent
(b) coincident
(c) consistent
(d) none of these
► (a) inconsistent

14. Find the solution to the following system of linear equations:
2x-5y+4 = 0 2x+y-8 = 0​
(a) (3,-2)
(b) (2,3)
(c) (-1,2)
(d) (3,2)
► (d) (3,2)

15. 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
► (d) passing through the origin

16. 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
► (a) a unique solution

17. 8 girls and 12 boys can finish work in 10 days while 6 girls and 8 boys can finish it in 14 days. Find the time taken by the one girl alone that by one boy alone to finish the work.
(a) 120, 130
(b) 140,280
(c) 240,280
(d) 100,120
► (b) 140,280

18. The graph of the equation 2x + 3y = 5 is a
(a) vertical line
(b) straight line
(c) horizontal line
(d) none of these
► (b) straight line

19. Two equations in two variables taken together are called
(a) linear equations
(c) simultaneous equations
(d) none of these
► (c) simultaneous equations

20. 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
► (b) y-axis

21. 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 – 14x + 4 = 0
(c) 10x – 14y = -4
(d) 10x + 14y + 4 = 0
► (c) 10x – 14y = -4

22. Find a and b for which (a - 1) x + 3y = 2, 6x + (1 - 2b) y = 6 infinite solution.​
(a) a = -7, b= -4
(b) a = -1, b = -4
(c) a = 3, b = -1
(d) a = 3, b = -4
► (d) a = 3, b = -4

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)
► (d) intersecting at (a, b)

24. The present age of a father is the sum of the ages of his three sons. Ten years from now his age will be a three quarter of the sum of their ages then. How old is the father?
(a) 50 years
(b) 30 years
(c) 40 years
(d) 60 years
► (a) 50 years

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

26. 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
► (a) 6

27. The pair of equations y = 0 and y = -7 has :
(a) no solution
(b) infinitely many solutions
(c) one solution
(d) two solutions
► (a) no solution

28. The graph of y = 5 is a line parallel to the
(a) x-axis
(b) y-axis
(c) both axis
(d) none of these
► (a) x-axis
X