s l e portion
Post on 22-May-2015
115 Views
Preview:
DESCRIPTION
TRANSCRIPT
SIMULTANEOUS LINEAR
EQUATIONS
12 34+ x ∛-
copyright : HARYANI JMSK
RECALL
copyright : bhhd_jmsk
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 ?
copyright : bhhd_jmsk
Do you know how
to find the
answers?
copyright : bhhd_jmsk
You will able to do this
after studying this chapter
32
1
CHAPTER REVIEW Linear
Equations
copyright : bhhd_jmsk
Simultaneous Linear Equations
Solving Methods
LINEAR EQUATIONS
copyright : bhhd_jmsk
An equation that relates numbers and linear terms involving the two variables
Example 3x + 6y = 5
Numbers
copyright : bhhd_jmsk
Variables Linear terms
SIMULTANEOUSLINEAR
EQUATIONS
copyright : bhhd_jmsk
4x – 3y = 3
A linear equations in two variables and the
variables are the same
Example 3x + 6y = 5
Two variablesSame variables
copyright : bhhd_jmsk
SOLVING METHODS
copyright : bhhd_jmsk
copyright : bhhd_jmsk
METHODS
Substitution Elimination
copyright : bhhd_jmsk
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
copyright : bhhd_jmsk
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
copyright : bhhd_jmsk
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 :
copyright : bhhd_jmsk
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
copyright : bhhd_jmsk
ELIMINATION METHOD
STEP 5Eliminate the variable STEP 6Find the value of y
- 2323 yx1293 yx_______________
3
2
232 y129 y_______________
5y
- 357 y
copyright : bhhd_jmsk
ELIMINATION METHOD
copyright : bhhd_jmsk
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
copyright : bhhd_jmsk
copyright : bhhd_jmsk
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 ?
copyright : bhhd_jmsk
The answer is ....
= RM 3.00
= RM 10.00
Let we see a complete solution ...
Still confused ?
copyright : bhhd_jmsk
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
copyright : bhhd_jmsk
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
copyright : bhhd_jmsk
THE END
copyright : bhhd_jmsk
THE END
REINFORCEMENT EXERCISE
copyright : bhhd_jmsk
REINFORCEMENT EXERCISE
Question 1
copyright : HARYANI JMSK
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 =
top related