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Simultaneous equations
 

Simultaneous equations

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    Simultaneous equations Simultaneous equations Presentation Transcript

    • 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 = 8 , Width = 2 ……………
    • 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 rectangle?
    • 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( x+y ) = 20 Its length is four times its width x = 4y
    • 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 cakes and tarts. Let x be the number of cakes Let y be the number of tarts
    • 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 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
    • 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. Let x be the age of the father Let y be the age of the son (Use tables please)
    • 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.
    • 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 rectangle? Length 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( x+y ) = 20 Its length is four times its width x = 4y
    • 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) into any one of the equation and solve it
    • 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 brother’s, how many stamps does each of them have?
    • 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 prices of a table and a chair?
    • 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 ratio became 3:5. How many candies did each of them get originally?
    • 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 ratio became 3:5.