Class 10 Maths – RD Sharma Chapter 3: Pairs of Linear Equations in Two Variables Exercise 3.5 Solutions (Step-by-Step Guide)

RD Sharma Chapter 3: Pairs of Linear Equations in Two Variables Exercise 3.5 Solutions

1. Determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it : x – 3y = 3, 3x – 9y = 2 Watch Solution
2. Determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it : 2x + y = 5, 4x + 2y = 10 Watch Solution
3. Determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it : 3x – 5y = 20, 6x – 10y = 40 Watch Solution
4. Determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it : x – 2y = 8, 5x – 10y = 10 Watch Solution
5. Find the value of k for which the following system of equations has a unique solution : kx + 2y = 5, 3x + y = 1 Watch Solution
6. Find the value of k for which the following system of equations has a unique solution : 4x + ky + 8 = 0, 2x + 2y + 2 = 0 Watch Solution
7. Find the value of k for which the following system of equations has a unique solution : 4x – 5y = k, 2x – 3y = 12 Watch Solution
8. Find the value of k for which the following system of equations has a unique solution : x + 2y = 3, 5x + ky + 7 = 0 Watch Solution
9. Find the value of k for which the system of equations has infinitely many solution : 2x + 3y – 5 =0, 6x +ky -15 =0 Watch Solution
10. Find the value of k for which the system of equations has infinitely many solution : 2x+3y-5=0, 6x+ky-15=0 Watch Solution
11. Find the value of k for which the system of equations has infinitely many solution : 4x+5y=3, kx+15y=9 Watch Solution
12. Find the value of k for which the system of equations has infinitely many solution : kx-2y+6=0, 4x-3y+9=0 Watch Solution
13. Find the value of k for which the system of equations has infinitely many solution : 8x+5y=9, kx+10y=18 Watch Solution
14. Find the value of k for which the system of equations has infinitely many solution : 2x-3y=7, (k+2)x – (2k+1)y = 3(2k-1) Watch Solution
15. Find the value of k for which the system of equations has infinitely many solution : 2x + 3y= 2, (k+2)x + (2k+1)y = 2(k-1) Watch Solution
16. Find the value of k for which the system of equations has infinitely many solution : x+(k+1)y =4, (k+1)x+ 9y=5k+2 Watch Solution
17. Find the value of k for which the system of equations has infinitely many solution : kx+3y= 2k+1 2(k+1)x +9y= 7k+1 Watch Solution
18. Find the value of k for which the system of equations has infinitely many solution : 2x+(k-2)y =k, 6x+(2k-1)y= 2k+5 Watch Solution
19. Find the value of k for which the system of equations has infinitely many solution : 2x+3y=7, (k+1)x+(2k-1)y=4k+1 Watch Solution
20. Find the value of k for which the system of equations has infinitely many solution : 2x+3y=k, (k-1)x+(k+2)y=3k Watch Solution
21. Find the value of k for which the following system of equations has no solution: kx-5y= 2, 6x +2y =7 Watch Solution
22. Find the value of k for which the following system of equations has no solution: x+2y = 0, 2x+ ky =5 Watch Solution
23. Find the value of k for which the following system of equations has no solution: 3x-4y+7=0, kx+3y-5=0 Watch Solution
24. Find the value of k for which the following system of equations has no solution: 2x-ky+3=0, 3x+2y-1=0 Watch Solution
25. Find the value of k for which the following system of equations has no solution: 2x+ky =11, 5x-7y =5 Watch Solution
26. Find the value of k for which the following system of equations has no solution: kx+3y =k-3, 12x+ky=6 Watch Solution
27. For what value of k the following system of equations will be inconsistent ? 4x+6y=11, 2x+ky=7 Watch Solution
28. For what value of α, the system of equations is inconsistent αx + 3y = α – 3, 12x + αy = α will have no solutions ? Watch Solution
29. Find the value of k for which the system kx+2y=5, 3x+y=1 has (i) a unique solution (ii) no solution. Watch Solution
30. Prove that there is a value of c(≠0) for which the system 6x+3y=c-3, 12x+cy=c Has infinitely many solutions. Find this value  Watch Solution
31. Find c if the system of equations cx+3y+3-c = 0 , 12x+cy-c = 0 has infinitely many solution ? Watch Solution
32. Find the values of k for which the system 2x+ky=1, 3x-5y=7 Will have (i) a unique solution and ii) no solution. Is there a value of k for which the system has infinitely many solutions ?  Watch Solution
33. For what value of k, the following system of equations will represent the coincident lines ? x+2y+7=0, 2x+ky+14=0 Watch Solution
34. Obtain the condition for the following system of linear equations to have a unique solution : ax + by=c, Ix+my=n Watch Solution
35. Determine the values of a and b so that the following system of linear equations have infinitely many solutions: (2a-1)x+3y-5=0, 3x+(b-1)y-2=0 Watch Solution
36. Find the values of a and b for which the following system of linear equations has infinite number of solutions: 2x-3y=7, (a+b)x-(a+b-3)y=4a+b Watch Solution
37. Find the values of p and q for which the following system of linear equations has infinite number of solutions: 2x+3y=9, (p+q)x-(2p-q)y = 3(p+q+1) Watch Solution
38. Find the values of a and b for which the following system of equations has infinitely many solutions : (2a-3)x -3y = 5 , 3x + (b-2)y = 3 Watch Solution
39. Find the values of a and b for which the following system of equations has infinitely many solutions : 2x- (2a+5)y = 5, (2b+1)x -9y = 15 Watch Solution
40. Find the values of a and b for which the following system of equations has infinitely many solutions : (a-1)x +3y = 2, 6x + (1-2b)y =6 Watch Solution
41. Find the values of a and b for which the following system of equations has infinitely many solutions : 3x+4y=12, (a+b)x +2(a-b)y =5a-1 Watch Solution
42. Find the values of a and b for which the following system of equations has infinitely many solutions : 2x+3y=7, (a-b)x +(a+b)y =3a+b-2 Watch Solution
43. Find the values of a and b for which the following system of equations has infinitely many solutions : 2x+3y-7= 0, (a-1)x +(a+1)y =3a-1 Watch Solution
44. Find the values of a and b for which the following system of equations has infinitely many solutions : 2x+3y=7, (a-1)x +(a+2)y =3a Watch Solution
45. Find the values of a and b for which the following system of equations has infinitely many solutions : x+2y =1, (a-b)x +(a+b)y =a+b-2 Watch Solution
46. Find the values of a and b for which the following system of equations has infinitely many solutions : 2x+3y=7, 2ax +ay =28-by Watch Solution
47. For which value(s) of λ, do the pair of linear equations λx + y = λ^2 and x +λy = 1 have (i) no solutions ? (ii) infinitely many solutions ? (iii) a unique solution ? Watch Solution

 

Pair of Linear Equations in Two Variables – R.D. Sharma Class 10th Math

1. Pair of Linear Equations in Two Variables Exercise 3.1 Video Solution

2. Pair of Linear Equations in Two Variables Exercise 3.2 Video Solution

3. Pair of Linear Equations in Two Variables Exercise 3.3 Video Solution

4. Pair of Linear Equations in Two Variables Exercise 3.4 Video Solution

5. Pair of Linear Equations in Two Variables Exercise 3.5 Video Solution

6. Pair of Linear Equations in Two Variables Exercise 3.6 Video Solution

7. Pair of Linear Equations in Two Variables Exercise 3.7 Video Solution

8. Pair of Linear Equations in Two Variables Exercise 3.8 Video Solution

9. Pair of Linear Equations in Two Variables Exercise 3.9 Video Solution

10. Pair of Linear Equations in Two Variables Exercise 3.10 Video Solution

11. Pair of Linear Equations in Two Variables Exercise 3.11 Video Solution

12. Pair of Linear Equations in Two Variables Multiple Choice Questions (MCQs) Video Solution Video Solution

13. Pair of Linear Equations in Two Variables Fill in the Blanks (FBQs) Video Solution

14. Pair of Linear Equations in Two Variables Very Short Answer Questions (VSAQs) Video Solution Video Solution