Oxford Mathematics for the New Century 2A
5 Linear Equations in Two Unknowns
Consolidation Exercise
5D
Level 1
Solve the following simultaneous equations by the method of elimination. [Nos. 116]
1.
 x  y  8

x  y  4
2.
6 x  11  y

3 x  16  y
3.
x  3 y  7

 x  y  5
4.
3 x  2 y  3

3 x  2 y  9
5.
 4 x  5 y  21

4 x  3 y  13
6.
3 x  5  4 y

5 x  13  4 y
7.
5c  d  7

3c  d  1
8.
h  10k  7

h  4k  25
9.
7 x  3 y  15

5 x  3 y  27
 x  3 y  14
10. 
3 y  x  28
4 y  3 x  15
11. 
3 x  4 y  9
3x  5 y  4
12. 
3x  7 y  16  0
4u  5v  29
13. 
4u  3v  21  0
8h  3k  7  0
14. 
8h  5k  31  0
15. a  b = 4a + b + 10 = 0
16. 2x + 5y  4 = 4x + 5y = 0
Solve the following simultaneous equations by any algebraic method. [Nos. 1722]
b  2a  5
17. 
a  b  7
m  2 n  1
18. 
m  5  2 n
a  7b  13
19. 
6a  7b  8
3s  5r  2
20. 
5r  2  s
 y  3  2x
21. 
2 y  33  5 x
5u  9v  2  0
22. 
5u  9v  2  0
© Oxford University Press 2021
5.1
Consolidation Exercise 2A Chapter 5
23. Determine whether the following simultaneous equations have no solutions or more than one
solution.
x  y  8
2 x  y  1
(a) 
(b) 
 x  y  12
2 x  y  1
3x  y  2
(c) 
3x  y  2
x  4 y  1  0
(d) 
 x  4 y  1
Solve the following simultaneous equations by any algebraic method. [Nos. 24–25]
x  2 y  7
 y  5  4x
24. 
25. 
 2 y  7  x
4 x  y  10
Level 2
Solve the following simultaneous equations by the method of elimination. [Nos. 2635]
3a  2b  13
26. 
a  3b  14
2h  k  3
27. 
3h  4k  10
3m  4n  2
28. 
 5m  2n  1
3 x  2 y  5
29. 
7 x  6 y  1
3 x  10 y  16
30. 
2 x  9 y  6
5 p  4q  3
31. 
4 p  5q  6
2 r  5 s  8
32. 
4 s  3r  34
a b
 5

4 3
33. 
a  b  7

3 2
34. 2x  y = 4x + 3y  5 = 0
35. 5a  14 = 2a + 5b  17 = 2b
© Oxford University Press 2021
5.2
Consolidation Exercise 2A Chapter 5
Solve the following simultaneous equations by any algebraic method. [Nos. 3645]
2 x  y  3  0
36. 
3x  4 y  1  0
2 x  5 y
37. 
6 x  10 y  3
 2h  k
5

38.  3
 h  3k  1
 4
2
m  3 n


39.  7
 4 m  2n  10  0

7
 p  0.5q  10
40. 
0.5 p  q  20
 x  6 y  4

41.  2
3
x y 5

5
5
2 x  3 y  4
42. 
4 x  6 y  8
24 x  18 y  11
43. 
7  8 x  6 y  0
44. 7k + 4(2  h) = 7h + 4k  14 = 0
45. 6r + 2s + 5(1  r) = 3(r + 2s) + 15 = 0
© Oxford University Press 2021
5.3
Consolidation Exercise 2A Chapter 5
Answers
Consolidation Exercise 5D
1. x = 2, y = 6
3. x = 11, y = 6
5. x = 4, y = 1
7. c = 4, d = 13
9. x = 6, y = 19
11. x = 1, y = 3
13. u = 6, v = 1
15. a = 2, b = 2
17. a = 4, b = 3
19. a = 1, b = 2
21. x = 3, y = 9
2. x = 3, y = 7
4. x = 1, y = 3
6. x = 1, y = 2
8. h = 37, k = 3
10. x = 7, y = 7
12. x = 3, y = 1
14. h = 2, k = 3
8
16. x = 2, y =
5
3
18. m = 2, n =
2
2
20. r = , s = 0
5
2
22. u = 0, v =
9
23. (a) no solutions
(b) more than one solution
(c) no solutions
(d) more than one solution
24. no solutions
25. more than one solution
26. a = 1, b = 5
27. h = 2, k = 1
1
28. m = 0, n = 
29. x = 1, y = 1
2
30. x = 12, y = 2
31. p = 1, q = 2
32. r = 6, s = 4
33. a = 12, b = 6
1
34. x = , y = 1
35. a = 4, b = 3
2
3
3
36. x = 1, y = 1
37. x = , y =
5
2
7
38. h = 7, k = 1
39. m =  , n = 4
2
11
40. p = 16, q = 12
41. x = 18, y =
3
42. more than one solution
43. no solutions
44. h = 2, k = 0
45. more than one solution
© Oxford University Press 2021
5.4
Consolidation Exercise 2A Chapter 5