1

Simultaneous Equations

2

Simultaneous: Happens at the same time Equations : x+1 = 4

3

4

5

Perimeter = ?

Length

Width

6

Perimeter = 20

Length

Width

7

Length = 3 , Width = 7 Length = 4 , Width = 6 Length = 5 , Width = 5 Length = 6 , Width = 4 Length = 7 , Width = 3 Length = 8 , Width = 2 ……………

8

Length 1 2 3 4

Width 9 8 7 6

5 6 7 8 9

5 4 3 2 1

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Perimeter = 20 Length>Width

Length

Width

10

Length 1 2 3 4

Width 9 8 7 6

5 6 7 8 9

5 4 3 2 1

Length>Width

11

Length 1 2 3 4

Width 9 8 7 6

5 6 7 8 9

5 4 3 2 1

Length>Width

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Perimeter = 20 Length = 4 x Width

Length

Width

13

Length 1 2 3 4

Width 9 8 7 6

5 6 7 8 9

5 4 3 2 1

Length = 4 x Width

14

Length 1 2 3 4

Width 9 8 7 6

5 6 7 8 9

5 4 3 2 1

Length = 4 x Width

15

Given the perimeter of a rectangle is

20 cm. If its length is four times its width, what is the dimension of the rectangle?

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The perimeter of a rectangle is 20 cm Its length is four times its width

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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

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2( x+y ) = 20

y = 4x

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20

19 Coins : $5 ,$10 $ 140

21

Number Value

$5 Coins

$10 Coins

Total

22

Number

$5 Coins x

$10 Coins y

Total

23

Number

$5 Coins x

$10 Coins y

Total x+y

24

Number Value

$5 Coins x

$10 Coins y

Total x+y

25

Number Value

$5 Coins x 5x

$10 Coins y 10y

Total x+y

26

Number Value

$5 Coins x 5x

$10 Coins y 10y

Total x+y 5x+10y

27

Number Value

$5 Coins x 5x

$10 Coins y 10y

Total 19 140

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Number Value

$5 Coins x 5x

$10 Coins y 10y

Total x+y=19 5x+10y=140

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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

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Number Eggs used

Cake

Tart

Total

31

Number Eggs used

Cake x

Tart y

Total

32

Number Eggs used

Cake x

Tart y

Total x+y

33

Number Eggs used

Cake x 2x

Tart y y/2

Total x+y

34

Number Eggs used

Cake x 2x

Tart y y/2

Total x+y 2x+y/2

35

Number Eggs used

Cake x 2x

Tart y y/2

Total 20 22

36

Number Eggs used

Cake x 2x

Tart y y/2

Total x+y=20 2x+y/2=22

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38

39

40

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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

42

43

Number

Win

Lose

Total

44

Number

Win a

Lose

Total

45

Number

Win a

Lose b

Total

46

Number

Win a

Lose b

Total a+b

47

Number Points

Win a

Lose b

Total a+b

48

Number Points

Win a 3a

Lose b

Total a+b

49

Number Points

Win a 3a

Lose b 1b

Total a+b

50

Number Points

Win a 3a

Lose b 1b

Total a+b 3a+b

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Number Points

Win a 3a

Lose b 1b

Total a+b=38 3a+b=92

52

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)

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1. 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.

2. 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.

3. 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.

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How to solve ??

1. Graphical method 2. Substitution 3. Elimination

(2,3 are algebraic methods)

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Method of Substitution

57

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

58

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

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If the length is 8 cm, what will y be?

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A number A variable

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2( x+y ) = 20 x = 4y

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2(x+y) = 20

x = 4y

2(4y+y) = 20

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OR

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a) Make x/y be the subject

b) Substitute the subjecting equation into the other one and solve it

c) Substitute the solution of (b) into any one of the equation and solve it

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Challenging Question

3x + 2y = 18

5x – 6y = -26

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Method of Elimination

$14.8

$18

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How much for only

one piece of filet?

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$18 $14.8 $3.2

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$ ??

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$18

$3.2

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$18 $3.2 $3.2 $11.6

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$3.2

$11.6

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2x +3y = 1 …… (1)5x – 3y = 34…… (2)(1) + (2)

2x +3y = 1+) 5x – 3y = 34

7x = 35

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3x +2y = 11 …… (1)x + y = 4 …… (2)

(2) x 22x + 2y = 8 …… (3)(1) - (2)

3x +2y = 11-) 2x + 2y = 8

x = 3

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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?

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Let x be the number of stamps the sister has

Let y be the number of stamps the brother has

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The brother and sister have altogether 48 stamps.

x + y =48 The sister has 16 stamps more than the

brother’s x – y = 16

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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?

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Let $x be the selling price of a table Let $y be the selling price of a chair

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3 tables and 4 chairs are sold at $6400 3x + 4y =6400 4 tables and 3 chairs are sold at $6900 4x + 3y =6900

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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?

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Let x be the respective number of candies Maggie has

Let y be the respective number of candies Charles has

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The original number of candies with Maggie and Charles was in the ratio of 9:7.

7

9

y

x

5

3

12

12

y

x

If Maggie gave 12 candies to Charles, the

ratio became 3:5.