s l e portion
DESCRIPTION
Notes on Simultaneous Linear Equation....TRANSCRIPT
SIMULTANEOUS LINEAR
EQUATIONS
12 34+ x ∛-
copyright : HARYANI JMSK
RECALL
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INTRODUCTION
Ali and Ah Chong buy fresh fruits from Mak Jah’s fruit stall. Ali buys six orange and four apples, which cost him RM58.00 while five orange and two apples that Ah Chong buys cost him RM35.00.
How much does each and
cost ?
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Do you know how
to find the
answers?
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You will able to do this
after studying this chapter
32
1
CHAPTER REVIEW Linear
Equations
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Simultaneous Linear Equations
Solving Methods
LINEAR EQUATIONS
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An equation that relates numbers and linear terms involving the two variables
Example 3x + 6y = 5
Numbers
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Variables Linear terms
SIMULTANEOUSLINEAR
EQUATIONS
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4x – 3y = 3
A linear equations in two variables and the
variables are the same
Example 3x + 6y = 5
Two variablesSame variables
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SOLVING METHODS
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METHODS
Substitution Elimination
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SUBSTITUTION
METHOD
2323 yx43 yx
_______________
STEP 1Write down the question
1
2
STEP 2Insert a label for each equation
STEP 3Select one of the equations
From equation 1
STEP 4Select one of the variables, then make it as a subject
yx 34
STEP 5Make the subject as a new equation
3
43 yx
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SUBSTITUTION
METHOD
Substitute x into2
STEP 6Substitute the variable into another equation2323 yx232)34(3 yy
STEP 7Solve the equation and find the value of y
357 y232912 yy
5y
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SUBSTITUTION
METHOD
Substitute y = 5 into3
STEP 8Select one of the appropriate equation
yx 34 )5(34 x
11x)15(4 x
STEP 9Substitute the value of y into the equation to get the value of x yx 34 3For example :
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ELIMINATION METHOD
2323 yx43 yx
_______________
STEP 1Write down the question
1
2
STEP 2Insert a label for each equation
STEP 3Select one type of variable to be eliminate
STEP 4Equate the both value
x 3
2323 yx1293 yx
_______________
3
2
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ELIMINATION METHOD
STEP 5Eliminate the variable STEP 6Find the value of y
- 2323 yx1293 yx_______________
3
2
232 y129 y_______________
5y
- 357 y
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ELIMINATION METHOD
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Substitute y = 5 into2
STEP 7Select one of the appropriate equation
2323 yx23)5(23 x
333 x10233 x
STEP 8Substitute the value of y into the equation to get the value of x 2323 yx 22For example :
11x
PRACTICE &
QUICK CHECK
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Have you already got the
answers ?
How much does each and
cost ?
Ali and Ah Chong buy fresh fruits from Mak Jah’s fruit stall. Ali buys six orange and four apples, which cost him RM58.00 while five orange and two apples that Ah Chong buys cost him RM35.00.
Do you remember
this question ?
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The answer is ....
= RM 3.00
= RM 10.00
Let we see a complete solution ...
Still confused ?
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Substitute = x
and = y
_______________6x + 4y = 58 ---------- 1
5x + 2y = 35 ---------- 2
Substitute x into 1
6x + 4y = 58
6+ 4y = 58
6 (35 – 2y) + 20y = 290
210 – 12y + 20y = 290
8y = 80
y =
y = 10
CHANGE THE FRUIT INTO THE VARIABLES
From equation 2
5x + 2y = 35x = 35 – 2y --------- 3
5
Substitute y = 10 into 3
x =
x =
x =
x = 3
Substitution Method
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Substitute = x
and = y
_______________6x + 4y = 58 ---------- 1
5x + 2y = 35 ---------- 2
CHANGE THE FRUIT INTO THE VARIABLES Elimination Method
6x + 4y = 58 ---------- 1
10x + 4y = 70 ---------- 3
x 2
- 4x = - 12
x =
x = 3
_______________-Substitute x = 3 into 1
6x + 4y = 58
6(3) + 4y = 58
18 + 4y = 58
4y = 58 – 18
4y = 40
y =
y = 10
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THE END
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THE END
REINFORCEMENT EXERCISE
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REINFORCEMENT EXERCISE
Question 1
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2x + 3y = 1 5x - 3y = 13
Answer : x = 2, y = -1
Question 23m – 2n = 10 6m + 7n – 9 = 0
Answer : m = , n = -1
Question 3e + 3f = 4 4e – 6f = 12
Answer : e = 4, f =