Upcoming SlideShare
×

# Simultaneous equations

937 views
825 views

Published on

0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total views
937
On SlideShare
0
From Embeds
0
Number of Embeds
6
Actions
Shares
0
51
0
Likes
0
Embeds 0
No embeds

No notes for slide

### Simultaneous equations

1. 1. Simultaneous Equations
2. 2. Simultaneous: Happens at the same time Equations : x+1 = 4
3. 3. Perimeter = ? Length Width
4. 4. Perimeter = 20 Length Width
5. 5. Length = 3 , Width = 7 Length = 4 , Width = 6 Length = 5 , Width = 5 Length = 6 , Width = 4 Length = 7 , Width = 3 Length = 8 , Width = 2 ……………
6. 6. 6 7 8 9 Width 4 3 2 1 Length 1 2 3 4 5 9 8 7 6 5
7. 7. Perimeter = 20 Length&gt;Width Length Width
8. 8. Length&gt;Width 6 7 8 9 Width 4 3 2 1 Length 1 2 3 4 5 9 8 7 6 5
9. 9. Length&gt;Width 6 7 8 9 Width 4 3 2 1 Length 1 2 3 4 5 9 8 7 6 5
10. 10. Perimeter = 20 Length = 4 x Width Length Width
11. 11. Length = 4 x Width 6 7 8 9 Width 4 3 2 1 Length 1 2 3 4 5 9 8 7 6 5
12. 12. Length = 4 x Width 6 7 8 9 Width 4 3 2 1 Length 1 2 3 4 5 9 8 7 6 5
13. 13. Given the perimeter of a rectangle is 20 cm. If its length is four times its width, what is the dimension of the rectangle?
14. 14. The perimeter of a rectangle is 20 cm Its length is four times its width
15. 15. Let x cm be the length of the rectangle and let y cm be the width of the rectangle The perimeter of a rectangle is 20 cm 2( x+y ) = 20 Its length is four times its width x = 4y
16. 16. 2( x+y ) = 20 y = 4x
17. 17. 19 Coins : \$5 ,\$10 \$ 140
18. 18. Total \$10 Coins \$5 Coins Value Number
19. 19. Total y \$10 Coins x \$5 Coins Number
20. 20. x+y Total y \$10 Coins x \$5 Coins Number
21. 21. x+y Total y \$10 Coins x \$5 Coins Value Number
22. 22. x+y Total 10y y \$10 Coins 5x x \$5 Coins Value Number
23. 23. 5x+10y x+y Total 10y y \$10 Coins 5x x \$5 Coins Value Number
24. 24. 140 19 Total 10y y \$10 Coins 5x x \$5 Coins Value Number
25. 25. 5x+10y=140 x+y=19 Total 10y y \$10 Coins 5x x \$5 Coins Value Number
26. 26. 2 eggs are required to bake a cake and ½ egg is required to bake a tart. A total of 22 eggs are used to bake altogether 20 cakes and tarts. Let x be the number of cakes Let y be the number of tarts
27. 27. Total Tart Cake Eggs used Number
28. 28. Total y Tart x Cake Eggs used Number
29. 29. x+y Total y Tart x Cake Eggs used Number
30. 30. x+y Total y/2 y Tart 2x x Cake Eggs used Number
31. 31. 2x+y/2 x+y Total y/2 y Tart 2x x Cake Eggs used Number
32. 32. 22 20 Total y/2 y Tart 2x x Cake Eggs used Number
33. 33. 2x+y/2=22 x+y=20 Total y/2 y Tart 2x x Cake Eggs used Number
34. 34. X Y 20
35. 35. 22 2X Y/2
36. 36. x+y=20 2x+y/2=22
37. 37. Arsenal played 38 matches in a league and got 92 points in total. It is known that each win scores 3 points, each draw scores 1 point, each loss scores 0 point, and Arsenal did not lose any game in the season. Let a be the number of wins Let b be the number of draws
38. 38. Total Lose Win Number
39. 39. Total Lose a Win Number
40. 40. Total b Lose a Win Number
41. 41. a+b Total b Lose a Win Number
42. 42. a+b Total b Lose a Win Points Number
43. 43. a+b Total b Lose 3a a Win Points Number
44. 44. a+b Total 1b b Lose 3a a Win Points Number
45. 45. 3a+b a+b Total 1b b Lose 3a a Win Points Number
46. 46. 3a+b=92 a+b=38 Total 1b b Lose 3a a Win Points Number
47. 47. The age of a father is now 3 times the age of his son. After 16 years, the age of father will be twice that of his son. Let x be the age of the father Let y be the age of the son (Use tables please)
48. 48. 3 balls and 4 books weigh 7.2 kg. 4 balls and 3 books weigh 6.8 kg. Let x kg and y kg be the weight of a book and a ball respectively. 5 kg of coffee and 2 kg of tea costs \$110, while 2 kg of coffee and 1 kg of tea costs \$50. Let \$x and \$y be the cost of coffee and tea respectively. A 2-digits number is equal to 4 times the sum of the 2-digits and the difference between the 2-digits is 3. Let x and y be the unit digit and tens digit respectively.
49. 49. How to solve ?? 1. Graphical method 2. Substitution 3. Elimination (2,3 are algebraic methods)
50. 50. Method of Substitution
51. 51. Given the perimeter of a rectangle is 20 cm. If its length is four times its width, what is the dimension of the rectangle? Length Width
52. 52. Let x cm be the length of the rectangle and let y cm be the width of the rectangle The perimeter of a rectangle is 20 cm 2( x+y ) = 20 Its length is four times its width x = 4y
53. 53. If the length is 8 cm, what will y be?
54. 54. A number A variable
55. 55. 2( x+y ) = 20 x = 4y
56. 56. 2(x+y) = 20 x = 4y 2(4y+y) = 20
57. 57. OR 3x-2y=12 2x+y=1 3x-2y=12 y=1-2x 3x-2y=12 x=(1-y)/2
58. 58. Make x/y be the subject Substitute the subjecting equation into the other one and solve it Substitute the solution of (b) into any one of the equation and solve it
59. 59. Challenging Question 3x + 2y = 18 5x – 6y = -26
60. 60. Method of Elimination \$14.8 \$18
61. 61. How much for only one piece of filet?
62. 62. \$18 \$14.8 \$3.2
63. 63. \$ ??
64. 64. \$18 \$3.2
65. 65. \$18 \$3.2 \$3.2 \$11.6
66. 66. \$3.2 \$11.6
67. 67. 2x +3y = 1 …… (1) 5x – 3y = 34 …… (2) (1) + (2) 2x +3y = 1 +) 5x – 3y = 34 7x = 35
68. 68. 3x +2y = 11 …… (1) x + y = 4 …… (2) (2) x 2 2x + 2y = 8 …… (3) (1) - (2) 3x +2y = 11 -) 2x + 2y = 8 x = 3
69. 69. Setting up the equations The brother and sister have altogether 48 stamps. If the sister has 16 stamps more than the brother’s, how many stamps does each of them have?
70. 70. Let x be the number of stamps the sister has Let y be the number of stamps the brother has
71. 71. The brother and sister have altogether 48 stamps. x + y =48 The sister has 16 stamps more than the brother’s x – y = 16
72. 72. 3 tables and 4 chairs are sold at \$6400, while 4 tables and 3 chairs are sold at \$6900. What are the respective selling prices of a table and a chair?
73. 73. Let \$x be the selling price of a table Let \$y be the selling price of a chair
74. 74. 3 tables and 4 chairs are sold at \$6400 3x + 4y =6400 4 tables and 3 chairs are sold at \$6900 4x + 3y =6900
75. 75. The original number of candies with Maggie and Charles was in the ratio of 9:7. If Maggie gave 12 candies to Charles, the ratio became 3:5. How many candies did each of them get originally?
76. 76. Let x be the respective number of candies Maggie has Let y be the respective number of candies Charles has
77. 77. The original number of candies with Maggie and Charles was in the ratio of 9:7. If Maggie gave 12 candies to Charles, the ratio became 3:5.