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Simultaneous Equations
Simultaneous:  Happens at the same time   Equations :  x+1 = 4
Perimeter = ? Length Width
Perimeter = 20 Length Width
Length = 3 , Width = 7 Length = 4 , Width = 6 Length = 5 , Width = 5  Length = 6 , Width = 4 Length = 7 , Width = 3 Length...
6 7 8 9 Width 4 3 2 1 Length 1 2 3 4 5 9 8 7 6 5
Perimeter = 20 Length>Width Length Width
Length>Width 6 7 8 9 Width 4 3 2 1 Length 1 2 3 4 5 9 8 7 6 5
Length>Width 6 7 8 9 Width 4 3 2 1 Length 1 2 3 4 5 9 8 7 6 5
Perimeter = 20   Length = 4 x Width Length Width
Length = 4 x Width 6 7 8 9 Width 4 3 2 1 Length 1 2 3 4 5 9 8 7 6 5
Length = 4 x Width 6 7 8 9 Width 4 3 2 1 Length 1 2 3 4 5 9 8 7 6 5
Given the perimeter of a rectangle is  20 cm. If its length is four times its width, what is the dimension of the rectangl...
The perimeter of a rectangle is 20 cm Its length is four times its width
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...
2( x+y ) = 20 y = 4x
19 Coins : $5 ,$10 $ 140
Total $10 Coins $5 Coins Value Number
Total y $10 Coins x $5 Coins Number
x+y Total y $10 Coins x $5 Coins Number
x+y Total y $10 Coins x $5 Coins Value Number
x+y Total 10y y $10 Coins 5x x $5 Coins Value Number
5x+10y x+y Total 10y y $10 Coins 5x x $5 Coins Value Number
140 19 Total 10y y $10 Coins 5x x $5 Coins Value Number
5x+10y=140 x+y=19 Total 10y y $10 Coins 5x x $5 Coins Value Number
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...
Total Tart Cake Eggs used Number
Total y Tart x Cake Eggs used Number
x+y Total y Tart x Cake Eggs used Number
x+y Total y/2 y Tart 2x x Cake Eggs used Number
2x+y/2 x+y Total y/2 y Tart 2x x Cake Eggs used Number
22 20 Total y/2 y Tart 2x x Cake Eggs used Number
2x+y/2=22 x+y=20 Total y/2 y Tart 2x x Cake Eggs used Number
X Y 20
22 2X Y/2
x+y=20 2x+y/2=22
Arsenal played 38 matches in a league and got 92 points in total. It is known that each win scores 3 points, each draw sco...
Total Lose Win Number
Total Lose a Win Number
Total b Lose a Win Number
a+b Total b Lose a Win Number
a+b Total b Lose a Win Points Number
a+b Total b Lose 3a a Win Points Number
a+b Total 1b b Lose 3a a Win Points Number
3a+b a+b Total 1b b Lose 3a a Win Points Number
3a+b=92 a+b=38 Total 1b b Lose 3a a Win Points Number
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.  L...
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 r...
How to solve ?? 1. Graphical method 2. Substitution 3. Elimination (2,3 are algebraic methods)
Method of Substitution
Given the perimeter of a rectangle is  20 cm. If its length is four times its width, what is the dimension of the rectangl...
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...
If the length is 8 cm, what will y be?
A number A variable
2( x+y ) = 20 x = 4y
2(x+y) = 20 x = 4y 2(4y+y) = 20
OR 3x-2y=12 2x+y=1 3x-2y=12 y=1-2x 3x-2y=12 x=(1-y)/2
Make x/y be the subject Substitute the subjecting equation into the other one and solve it Substitute the solution of (b) ...
Challenging Question 3x + 2y = 18 5x – 6y = -26
Method of Elimination $14.8 $18
How much for only    one piece of filet?
$18 $14.8 $3.2
$ ??
$18 $3.2
$18 $3.2 $3.2 $11.6
$3.2 $11.6
2x +3y = 1 ……  (1) 5x – 3y = 34 …… (2) (1) + (2) 2x +3y  = 1 +) 5x – 3y = 34  7x   = 35
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
Setting up the equations The brother and sister have altogether 48 stamps. If the sister has 16 stamps more than the broth...
Let x be the number of stamps the sister has Let y be the number of stamps the brother has
The brother and sister have altogether 48 stamps. x + y =48 The sister has 16 stamps more than the brother’s x – y = 16
3 tables and 4 chairs are sold at $6400, while 4 tables and 3 chairs are sold at $6900. What are the respective selling pr...
Let $x be the selling price of a table  Let $y be the selling price of a chair
3 tables and 4 chairs are sold at $6400 3x + 4y =6400 4 tables and 3 chairs are sold at $6900  4x + 3y =6900
The original number of candies with Maggie and Charles was in the ratio of 9:7. If Maggie gave 12 candies to Charles, the ...
Let x be the respective number of candies Maggie has Let y be the respective number of candies Charles has
The original number of candies with Maggie and Charles was in the ratio of 9:7. If Maggie gave 12 candies to Charles, the ...
Simultaneous equations
Simultaneous equations
Simultaneous equations
Simultaneous equations
Simultaneous equations
Simultaneous equations
Simultaneous equations
Simultaneous equations
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Transcript of "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>Width Length Width
  8. 8. Length>Width 6 7 8 9 Width 4 3 2 1 Length 1 2 3 4 5 9 8 7 6 5
  9. 9. Length>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.
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