Assignment - Linear Equation in two Variables, Class 10 Mathematics PDF Download

VERY SHORT ANSWER TYPE QUESTIONS

Based on Consistency/Inconsistency of the system

1. On comparing the ratios out whether the following pair of linear equations are consistent or inconsistent.

(i) x – 3y = 4 ; 3x + 2y = 1          (ii) 4/3 x + 2y = 8 ; 2x + 3y = 12
(iii) 4x + 6y = 7 ; 12x + 18y = 21       (iv) x – 2y = 3 ; 3x – 6y = 1

2. On comparing the ratios   find out whether the lines representing the following pair of linear equations intersect at a point, are parallel or coincident :

(a) (i) 2x – y = 3 ; 4x – y = 5 (ii) x + 2y = 8 ; 5x – 10y = 10 (iii) 3x + 4y = – 2 ; 12x + 16y = – 8
(b) (i) 6x + 3y = 18 ; 2x + y = 6 (ii) x – 3y = 3 ; 3x – 9y = 2 (iii) ax – by = c1 ; bx + ay = c₂, where a  0, b 0

3. For the linear equations given below, write another linear equation in two variables, such that the geometrical representation of the pair so formed is  
(i) Intersecting lines (ii) Parallel lines (iii) Coincident lines
(a) 2x – 3y = 6 (b) y = 2x + 3

4. Find the value of k for which the given system of equations has a unique solution.
(a) (k – 3)x + 3y = k ; kx + ky = 12 (b) x – ky = 2; 3x + 2y = – 5

5. Find the value of k for which the given system of equations has no solution.
(a) kx + 2y – 1 = 0 ; 5x – 3y + 2 = 0
(b) (i) x + 2y = 3 ; 5x + ky + 7 = 0 (ii) kx + 3y = k – 3 ; 12x + ky = k

6. (a) Find the value(s) of k for which the system of equations kx – y = 2 and 6x – 2y = 3 has
(i) A unique solution (ii) No solution
(b) Find the value of k for which system kx + 2y = 5 and 3x + y = 1 has
(i) A unique solution (ii) No solution

7. Find the value of k for which the given system of equations has an infinite number of solutions.
(a) 5x + 2y = 2k and 2(k + 1) x + ky = (3k + 4)
(b) (i) x + (k + 1)y = 5 and (k + 1)x + 9y = 8k – 1
(ii) 10x + 5y – (k – 5) = 0 and 20x + 10y – k = 0
(c) kx + 3y = k – 3 and 12x + ky = k

8. Find the value of a and b for which the given system of linear equation has an infinite number of solutions :
(a) 2x + 3y = 7 and (a – b) x + (a + b) y = 3a + b – 2
(b) (a + b)x – 2by = 5a + 2b + 1 and 3x – y = 14
(c) (2a – 1)x + 3y – 5 = 0 and 3x + (b – 1)y – 2 = 0

SHORT ANSWER TYPE QUESTIONS
Based on graphical solution of system of equations :

Solve graphically each of the following pairs of equations (1-9) :
1. x + y = 4, 2x – 3y = 3

2. x + y = 3, 2x + 5y – 12 = 0

3. 4/9 x + 1/3 y = 1, 5x + 2y = 13

4. 2x + 3y = 4, x – y + 3 = 0

5. x + y = 7, 5x + 2y = 20

6. x + 4y = 0, 2x + 8y = 0

7. x + 2y = 3, 2x + 4y = 15

8. 3x + 2y = 3, 6x + 4y = 15

9. 2x + 3y – 5 = 0, 6x + 9y – 15 = 0

10. Check whether the pair of equations x + 3y = 6, and 2x – 3y = 12 is consistent. If so, solve graphically.

11. Show graphically that the pair of equations 2x – 3y + 7 = 0, 6x – 9y + 21 = 0 has infinitely many solutions.

12. Show graphically that the pair of equations 8x + 5y = 9, 16x + 10y = 27 has no solution.

13. Find whether the pair of equations 5x – 8y + 1 = 0, 3x - 24/5y+3/5 =0 has no solution, unique solution or
infinitely many solutions.

14. Show graphically that the pair of equations 2x – 3y = 4, 3x – 2y = 1 has a unique solution.

15. Show graphically that the pair of equations 3x + 4y = 6, 6x + 8y = 12 represents coincident lines.

16. Determine by drawing graphs whether the following pair of equations has a unique solution or not : 2x – 3y = 6, 4x – 6y = 9. If yes, find the solution also.

17. Determine graphically whether the pair of linear equations 3x – 5y = – 1, 2x – y = – 3 has a unique solution or
not. If yes, find the solution also.

18. Solve graphically the pair of equations x + 3y = 6, and 3x – 5y = 18. Hence, find the value of K if 7x + 3y = K.

19. Solve graphically the pair of equations 2x – y = 1, x + 2y = 8. Also find the points where the lines meet the axis
of y.

20. Solve graphically the following pair of linear equations : 2x + 3y – 12 = 0, 2x – y – 4 = 0. Also find the coordinates of the points where the lines meet the y-axis.

21. Solve the following pair of equations graphically : x + y = 4, 3x – 2y = – 3 Shade the region bounded by the lines representing the above equations and x-axis.

22. Solve the following pair of linear equations graphically : 2x + y = 8, 3x – 2y = 12. From the graph, read the points where the lines meet the x-axis.

23. Solve graphically the following pair of equations : x – y = 1, 2x + y = 8. Shade the area bounded by these lines and
the y-axis.

24. On the same axes, draw the graph of each of the following equations : 2y – x = 8, 5y – x = 14, y – 2x = 1. Hence, obtain the vertices of the triangle so formed.

25. Solve graphically the pair of linear equations : 4x – 3y + 4 = 0, 4x + 3y – 20 = 0. Find the area of the region bounded by these lines and x-axis. 

Based on substitution method :
Solve the following equations by the substitution method : (26-41)

26. 3x + 11y = 13, 8x + 13y = 2

27. x + 2y = 1.6, 2x + y = 1.4

28. 11x – 8y = 27, 3x + 5y = – 7

29. 0.04 x + 0.02y = 5, 0.5x – 0.4y = 30

30. 5x + 8y = – 1, 6y – x = 4y – 7

31. 12x – 16y = 20, 8x + 6y = 30

32. 8x – 5y + 40 = 0, 7x – 2y = 0

33. 1/2 (9x + 10y) = 23, 5x/4  – 2y = 3

34. 

35. 

36. 3x + 15 = 4y, 3y + 17 = 2 + 3x
37. x + 6y = 2x – 16, 3x – 2y = 24
38. x = 3y – 19, y = 3x – 23
39. 5x + 2y = 14, x + 3y = 8

40. 

41. 

42. Solve 2x – y = 12 and x + 3y + 1 = 0 and hence find the value of m for which y = mx + 3.
43. Solve 4x – 3y + 17 = 0 and 5x + y + 7 = 0 and hence find the value of n for which y = nx – 1.