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Notes on Simultaneous Linear Equation....

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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 =

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