RANGKUMAN MAT.WAJIB 1

SISTEM PERSAMAAN LINIER TIGA VARIABEL (SPLTV)

Sistem persamaan linear 3 variabel, merupakan himpunan 3 buah persamaan dengan variabel sebanyak 3. Bentuk ini satu tingkat lebih rumit dibandingkan sistem persamaan linear 2 variabel

Metoda meyelesaikan persamaan

1. Metoda Eliminasi

2. Metoda subtitusi

3. Metoda determinan

4. Metoda matriks

5. Metoda operasi baris elementer

 

Metoda Eliminasi

Supaya lebih mudah langsung saja kita masuk ke contoh-contoh

Contoh soal 1 :

2x + 3y – z = 20

3x + 2y + z = 20

x + 4y + 2z = 15

Jawab :

Ketiga persamaan bisa kita beri nama persamaan (1), (2), dan (3)

2x + 3y – z = 20 ………………………..(1)

3x + 2y + z = 20 ………………………..(2)

x + 4y + 2z = 15 ………………………..(3)

Sistem persamaan ini harus kita sederhanakan menjadi sistem persamaan linear 2 variabel. Untuk itu kita eliminasi variabel z

Sekarang persamaan (1) dan (2) kita jumlahkan

2x + 3y – z = 20

3x + 2y + z = 20_____   +

5x + 5y = 40

x + y = 8 ………………….(4)

Selanjutnya persamaan (2) dikali (2) dan persamaan (3) dikali (1) sehingga diperoleh

6x + 4y + 2z = 40

x + 4y + 2z = 15____  _

               5x = 25

                 x = 5

Nilai x ini kita subtitusi ke persamaan (4) sehingga

x + y = 8

5 + y = 8

       y = 3

selanjutnya nilai x dan y yang ada kita subtitusikan ke persamaan (2)

3x + 2y + z = 20

3.5 + 2.3 + z = 20

15 + 6 + z = 20

               z = -1

Jadi, himpunan penyelesaiannya adalah {(5, 3, -1)}

Contoh soal 2 :

Tentukan himpunan penyelesaian dari

3x + 4y – 3z = 3

2x – y + 4z = 21

5x + 2y + 6z = 46

Jawab :

Agar lebih mudah, ketiga persamaan kita beri nama (1), (2), dan (3)

3x + 4y – 3z = 3  …………………………….(1)

2x – y + 4z = 21  …………………………….(2)

5x + 2y + 6z = 46 …………………………….(3)

Selanjutnya persamaan (1) dikali 1 dan persamaan (2) dikali 4, sehingga diperoleh

3x + 4y – 3z = 3    |1| → 3x + 4y – 3z = 3

2x – y + 4z = 21    |4| → 8x – 4y+16z = 84    +

.                                  11x + 13z = 87 ……………..(4)

Berikutnya persamaan (3) dikali 1 dan persamaan (2) dikali 2, sehingga diperoleh

5x + 2y + 6z = 46    |1| → 5x + 2y + 6z = 46

2x – y + 4z = 21      |2| → 4x – 2y + 8z = 42     +

.                                    9x + 14z = 88 …………..(5)

Sekarang persamaan (5) dikali 11 dan persamaan (4) dikali 9 sehingga diperoleh

9x + 14z = 88   |11|   99x +154z = 968

11x + 13z = 87  |9|    99x + 117z=783       _

.                                      37z = 185

.                                          z = 5

Nilai z=5 kita subtitusi ke persamaan (4)

11x + 13z = 87

11x + 13.5 = 87

11x + 65 = 87

         11x = 22

              x = 2

Nilai x=2 dan z=5 kita subtitusikan ke persamaan (3) sehingga

5x +2y +6z = 46

5.2 +2y +6.5 = 46

10 + 2y + 30 = 46

                  2y = 6

                    y = 3

Jadi, himpunan penyelesaiannya adalah {(2, 3, 5)}























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RANGKUMAN B.ING 1

BAB I
Hasil gambar untuk bahasa inggris
A.   Greeting Someone
Greetings
Responses
• Good morning.
• Good afternoon.
• Good evening.
• How nice to see you
• Hello.
• How are you?
• How do you do?
• How’re you doing?
• Hi!
• Good morning.
• Good afternoon.
• Good evening.
• Yes, it’s been so nice.
Hello.
• Fine, thanks.
• How do you do?
• Not bad.
• Hi!
 Examples in dialogue:
Dialogue 1
Ranti meets her teacher, MrBakri at the post office.
Ranti :Good afternoon, Sir.
MrBakri : Good afternoon. You are ….
Ranti :Ranti, Sir. My name is Ranti. How are you?
MrBakri : I am fine, thank you. And how about you?
Ranti : I am fine, too.
MrBakri : Well, Ranti. I have to go now. Pleased to meet you.
Ranti : Pleased to meet you, too, Sir.
B.    Parting Someone
Partings
Responses
• Good night.
• Goodbye.
• See you later.
• Bye
• Good night.
• Goodbye.
• See you.
• Bye.
 Examples in dialogue:
Dialogue 2
Andi : Good morning. My name is Andi.
Denias : Good morning Andi. I’m Denias.
Andi :Denias, this is Adib. We were classmates the Junior High School.
Denias : Hi, Adib. How do you do?
Adib : How do you do.
Andi : By the way, did you join pencaksilat extracurricular activity in the Junior High School?
Denias : Yes, I did.
Andi : Oh, that’s great. Adib and I have never joined it before.
Adib : We hope you can help us.
Denias : Sure.
Andi : Okay, see you this afternoon.
Adib : See you Denias.
Denias :See you.
C.  Introducing Yourself and Introducing Someone

Introducing Yourself
Introducing Someone
• First let me introduce myself.
• My name is ….
• Allow me to introduce my self.
• I’m …
• Excuse me my name’s…
• How do you do? My name is ….
• Hi! I’m …
• Hello! My name is …
• Good morning. My name’s …
• I would like to introduce you to ….
• Let me introduce you to …
• This …
• Allow me to introduce ….
• I’d like you to meet …
• Do you know …
• Oh look, here’s Peter.
• Peter–Jeny, Jeny–
Peter

Example in dialogue:
Stacey: I don’t think we’ve met. I’m Stacey. (hold out hand to shake)
Carl: Hi Stacey. I’m Carl.
Stacey: Hi Carl. So, how do you know Jane?
Carl: Oh, Jane and I used to work together at a coffee shop.
Stacey: Oh, you mean when you were working in Japan?
Carl: That’s right. And how do you know her?
Stacey: Actually, Jane is my cousin. Our moms are sisters.
Carl: No way! You two don’t look anything alike.
 D.   Genre: Recount Texts
  • Social function : to retell events for the purpose of informing or entertaining
  • Generic structure
– Orientation : provides the setting and introduces participants
– Events : tell what happened, in what sequence
– Re-orientation : optional-closure of events
  • The Characteristics of Recount Text:
  • Using the simple past tense, past continuous tense, past perfect tense, and past perfect continuous tense.
  • Using the conjunctions, such as: then, before, after, etc


BAB II
A.           Showing Happiness
Expressing Happiness is an expression that is used to show that someone or people are glad have excited feelings.
• It’s really great. I’m so happy.
• I’m delighted to hear that.
• It gives me a great pleasure.
• Nice news! Or good News! It makes me happy.
• Hooray!
• It’s lovely.

Example in dialogue:
Grace              : Hello, Anthony! I just knew that you have a cat.
Anthony         : Hello Grace! I do. Mr. Ridwan gave me this cat two days ago. I’m so happy about it. You know, I really want to have a cat.
Grace              : It is really pretty.
 B.  Showing Affection (Giving Attention)
Giving attention is an expression to give attention or show your affection to somebody. You give attention to someone when he/she looks sad, pale or wears nice thing or to react of a deliberation.
• What should I do to cheer you up?
• I really care about you?
• Don’t you worry. I’m with you.
• What’s wrong with you?
• Hope you will be fine.
• Are you OK?

Example in dialogue:
Rina     : Hi, Annisa.
Annisa : Hi.
Rina     : You look sad. What’s wrong with you ?
Annisa : Yes, I’m sad. Because, my mother has  just hospitalized now. I’m worrying her.
Rina     : Oh.. I’m sad too. Wish your mother get well soon.
Annisa : Thank you.
The underline-typed sentence in the dialog is used to give attention.
C.  Showing Sympathy
Expressing sympathy is used to expressing sympathy feeling on care to someone who has problem or accident.
• You have my deepest sympathy.
• What a terrible situation for you.
• I do sympathise (I assure you).
• I’m extremely sorry to hear that.
• I know how it feels
• Oh what a shame ….
• Oh that’s awful.
• Oh dear, sorry to hear that.
Example in dialogue:
Rina : Hi, Doni. What’s up? You look so sad.
Doni : Yea, my grandpa died last night.
Rina : Really? I’m sorry to hear that.
Doni : Thanks.
Rina : If I’m not mistaken, he is in Bandung, right?
Doni : Yes. We haven’t visited him yet.
Rina : Does your family plan to go to Bandung?
Doni : Yes. Tonight. We are going to leave for Bandung.
Rina : Oh, I hope your family will be fine.
Doni : Thanks a lot, Rina.
D.   Genre: Narrative Text
  • Social Function : to amuse, entertain and to deal with actual or vicariousexperience in different ways.
    • Generic Structure
– Orientation : sets the scene and introduces the participants.
– Complication : a crisis arises.
– Resolution : the crisis is resolved, for better or for worse.
  • Language features :
–      Past tense (killed, drunk,etc)
–      Adverb of time (Once upun a time, one day, etc)
–      Time conjunction (when, then, suddenly, etc)
–      Specific character. The character of the story is specific, not general. (Cinderella, Snow White, Alibaba, etc)
–      Action verbs. A verb that shows an action. (killed, dug, walked, etc)
Direct speech. It is to make the story lively. (Snow White said,”My name is Snow White). The direct speech uses present tense

BAB III
A.   Expressions of inviting, accepting, decliningan invitation and an appointment. 
Inviting
Accepting an Invitation
Declining an Invitation
• Would you like to ….
• I’d very much like
you to ….
• We should be
pleased/delighted if
you could ….
• Would you care to ….
• You will … won’t you?
• That’s very kind of you.
• We’d very much like
to ….
• What a delightful idea.
• With the greatest
pleasure.
• Thank you very much
for inviting me
• I’m very sorry, I don’t
think I can.
• I’d like to, but ….
• I’m afraid I’ve
already promised ….
• Thank you for asking
me, but ….
• Unfortunately, I can’t
….
 Example in dialogue:
Ludi  :  Hi, Maya. There will be a great film tonight. It’s about vampire. Would you like to go to the movie with me?
Maya :I don’t think I can. I’m doing my homework. My parents won’t let me out before I finish my homework.
Ludi : How about tomorrow night?
Maya  : Yes, I’d like to very much. When will you pick me up?
Ludi   :  I’ll pick you at 7.00. Be ready, OK!
Maya   : Alright.
B.   Expressing of Making, Accepting, and Cancelling an Apointment
Making an Appointment
Accepting an Appointment
Cancelling an Appointment
• How about tomorrow
morning?
• Let’s meet at … o’clock.
• I’ll come I promise.
• I’ll be there.
• Sorry, I don’t think I
can make it.
• I’m so sorry I can’t
make it.
 Example in dialogue:
 Linda     : Anna, are you doing anything tonight?
Anna     : Not really. Why?
Linda     : i’m going to a movie tonight. I wonder if you want to come with me.
Anna     : What kind of movie is it?
Linda     : it’s an action movie.
Anna     : no, thanks. I’m not really into action movie.
Linda        : What about having dinner?. My mother is going to go to Jakarta with my father tonight. I cannot cook.
Anna        : Oh, sure. Where?
Linda        : I heard Roka restaurant is excellent. Do you want to go there?
Anna        : sounds good.
Linda        : Okay. I’ll pick you up at your house at seven.
Anna        : Okay. See you then. 
C. Genre: Procedure
  • Social function : to describe how something is accomplished through a sequenceof actions or steps.
  • Generic structure:
    1. Goal: showing the purpose
    2. Material: Telling the needed materials
    3. Steps: Describing the steps to achieve the purpose
  • Language Feature of Procedure:
  1. Using temporal conjunction
  2. Using action verb
  3. Using imperative sentence
  4. Using Simple Present Tense
A.   Functional Text : Invitation Letter
An invitation letter is just what the term implies, it’s an invitation to something. It can be an invitation to:
-a celebration
-a special function
-an open house
-a company function
-an introduction of a new product or program to take advantage of a special offer 

BAB IV
A.   Congratulating someone
Congratulation is an expression that we use to give the congratulation utterance when he or she succeeds in doing something.
Congratulating
Responding
o   I’d be the first to congratulate you on…
o   I’d like to congratulate you on …
o   Please accept my warmest congratulations.
o   May I congratulate you on …
o   I must congratulate you.
o   It was great to hear about …
o   Congratulations.
o   Congratulations on …
o   Well done
o   Nice done, congratulations!
o   Good.
o   Fantastic!
o    It’s very good of you to say so.
o    How nice of you to say so.
o    Thank you very much for saying so.
o    I’m glad you think so.
o    Oh, it’s nothing special actually.
o    Oh, I have a lot to learn yet.
o    Thank you.
o    Oh, not really.
o    Oh, nothing to it, actually.
o    Oh, thanks.
Example in dialogue:
Asti          : I heard you graduated with honors. Congratulations! You did it!
Bob          : Thanks a lot!
Asti          : What are you going to do next? Get a job?
Bob          : No, I am going to the States next month to get my Master’s.
Asti          : That’s great! Go for it! Good luck!
Bob          : Thanks!
B.    Complimenting someone
Compliment is an expression that we show or say to express or give praise.
Complimenting someone
Responding
o   I would like compliment you on …
o   I think your ……. is very nice.
o   I just love your ……
o   The …… is very delicious.
o   I really like your …….
o   You look fabulous!
o   Fantastic!/Marvelous!
o   That’s nice.
o   That’s not bad.
o   Perfect!
o   Pretty good.
o   Thank you. It’s nice of you to say so.
o   Thank you but really isn’t anything special.
o   Thank you. Yours is even nicer.
o   I’m glad you like it.
o   Thank you.
o   Thank you so much.
o   Yeah, thanks.
Example in dialogue:
Sarah     : Jasmine, This is dress for you. I made it   by myself .
Jasmine  :That’s a beautiful dress! You are really a talented tailor.
Sarah     : I’m glad you like it.
BAB V
A.   Expressing Gratitude
Gratitude is an expression that we show or say to express grateful feeling to other people.
Expressing gratitude
Responding
o   I’m so grateful for ……
o   Thank you for ……
o   Thanks a lot.
o   Thanks a million.
o   Thanks./Many thanks.
o   Thank you very much for …..
o   Thank you for your help.
o   I’m really very grateful to you.
o   Thank you so much.
o   You’re welcome
o   Don’t mention it
o   My pleasure
o   I’m glad that I can help you.
o   It’s all right.
o   That’s what friends are.
o   It was my pleasure.
o   Yaps, never mind.
 Example in dialog:
John           : Can you help me to take that book?
Michael       : Yes, of course. This is, John.
John           : Thank you so much for your helping.
Michael       : You’re welcome.
 B.    Descriptive Text
  • Function : to describe a particular person, place or thing.
  • Generic Structure:
a. Identification : identifies phenomenon to be described.
b. Description : describes parts, qualities, characters.
  • Language Features:
    1. Use simple present tense.
    2. Use any kind of adjectives to describe the characteristic of person or thing or place.
    3. Use the relating verbs.
    4. Use thinking verbs and feeling verbs.
    5. Use adverbs.
A.   Functional Text : Announcement
  • Announcement is something said, written, or printed to make known what has happened or what will happen.
  • Points of announcement are:
1. Head (the title or type of event)

2. Closing (For more information,….) 
3. Body or content (date, place, program, etc)
4. Writer (someone or an institution who make the announcement)
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