Chapter4 Linear Equation

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CHAPTER 4:LINEAR EQUATION

SUBTOPICS:4.1 LINEAR EQUALITY4.2 LINEAR EQUATIONS IN ONE

UNKNOWN4.3 SOLUTIONS OF LINEAR EQUATIONS IN

ONE UNKNOWN



4.1 LINEAR EQUALITY

The symbol ¶=· is read as ¶is equal to·.² For example,

a)1cm = 10mmb)4 ² 2 = 5 ² 3 The symbol ¶· is read as ¶is not equal to·.

² For example,a)1cm 30mmb)4 ² 2 5



If a = b and b = c, then a = c

-For example,a) 2 + 4 = 6 and 6 = 7 ² 1, then 2 + 4 = 7 ² 1



Exercise Subtopic 4.1

1) 4 + 5 16 ² 7

2) 8m ² m 10m ² 3 m

3) 3n +4m 7nm

4) 5p + p 6p -p



4.2 LINEAR EQUATIONS IN ONE

UNKNOWN A linear algebraic term is an algebraic term

that consists of only one unknown and this

unknown is power of 1.For example, 2x, 3y, 4p, -5q, -0.3m

A linear algebraic expression is acombination of linear algebraic terms byaddition or subtraction.

For example, 2x + 3y, 4p-5q+7



A linear equation is an equation that

consists of only linear algebraic terms.For example, 2x + 3y = 0, 4p-5q+7=3

A linear equation in one unknown consistsof only one unknown in the equation.For example, y ² 7 = 25




Determine whether each of the following is alinear equation in one unknown.

a) 3x -4x = 6

b) -5xy-x = 3y



c) 5x ² 4 = 7 ² 2x

d) 5x ² 4

e) 3m + 2= 0




1)Solvea)x + 3 = -7

b)x ² 8 = - 10



Exercise of Chapter 4

1) Given that 3m + 29 = 53 - m, then m =



2) Given that 3p = 13 - (2p + 3), then p =



3) Given that 7y-9=3-5y, then y=

(NO. 9, 93)



4) Given that 3x + y = 8 and x - y = 4, then y =



5) Given that 2x + 3y = 18 and 2x - 3y = -6, then x + y =

(NO. 48, 93)



6) Fauzi wants to solve simultaneous equation4x + y = 7 dan 3x - 2y = 8. The steps are as below:

The blank must be filled with ___________

(NO. 38, 96)

12x + 3y = 2112x -8y = 32

= -11



END OF CHAPTER 4




1) 4 + 5 16 ² 79 = 9

2) 8m ² m 10m ² 3 m7m = 7 m

3) 3n +4m 7nm

4) 5p + p 6p -p6p 5p

=

=




Determine whether each of the following is alinear equation in one unknown.

a) 3x -4x = 63x -4x²= 6 is not a linear equation in one

unknown.(4x² is not a linear algebraic term)

b) -5xy-x = 3y-5xy-x = 3y is not a linear equation in one

unknown.(4x² is not a linear algebraic term)



c) 5x ² 4 = 7 ² 2x5x ± 4 = 7 ± 2x is a linear equation in one

unknown.(7x ± 4 = 7 )

d) 5x ² 45x ± 4 is not a linear equation in one unknown. (It

is a linear algebraic expression)

e) 3m + 2= 03m + 2= 0 is a linear equation in one unknown.




1)Solvea)x + 3 = -7

b)x ² 8 = - 10

x + 3 - 3 = - 7 - 3

x = - 10

x - 8 + 8 = - 10 + 8x = - 2



Exercise of Chapter 4

1) Given that 3m + 29 = 53 - m, then m =

3m + 29 = 53 ² m

3m + m+29 -29= 53 ² m+m-293m + m= 53 ² 294m=24

m= 4

24

m=6



2) Given that 3p = 13 - (2p + 3), then p =

3p = 13 - (2p + 3)

3p=13-2p-3

3p+2p=13-35p=10

p=5

10

P=2



3) Given that 7y-9=3-5y, then y=

7y-9=3-5y

7y+5y=3+9

12y=12y=

12

12

y=1

(NO. 9, 93)



4) Given that 3x + y = 8 and x - y = 4, then y =

x-y=4x=4+y «««..(1)

(1) in (2): 3(4+y)+y=8

3x + y = 8 «««.(2)

12+4y=812+3y+y=8

4y=8-12

4y=-4y=

4

4

y=-1



5) Given that 2x + 3y = 18 and 2x - 3y = -6, then x + y =

2x+3y=18 «««..(1)

(1) + (2): 2x+2x=18-62x-3y=-6 «««.(2)

4x=12x=

4

12

x=3

x=3 in (1): 2(3)+3y=186+3y=18

3y=18-63y=12y=

3

12

y= 4

x+y=3+4

x+y=7

(NO. 48, 93)



6) Fauzi wants to solve simultaneous equation4x + y = 7 dan 3x - 2y = 8. The steps are as below:

The blank must be filled with ___________

(NO. 38, 96)

12x + 3y = 2112x -8y = 32

= -11

21-32=-11, therefore 3y-(-8y)=3y+8y

So, the answer is 11y

Solution:

=11y

Chapter4 Linear Equation

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