Grade 8 - Chapter 4 - SLETV/SPLDV Part 7

Systems of Linear Equation in Two Variables (SLETV)

Sistem Persamaan Linear Dua Variabel (SPLDV)

Standard of Competence :

2.  Understanding System of Linear Equation in Two variables and Using it in problem solving

Memahami SPLDV dan menggunakannya dalam pemecahan masalah

Basic Competence :

2.3 Making mathematics models from daily life that related with LESTV

Membuat model matematika dari peristiwa sehari – hari yang sesuai dengan SPLDV.

Learning Objective :

1.       Students are able to make mathematics models from daily life related with SLETV

Siswa dapat membuat model matematika dari peristiwa sehari-hari yang sesuai dengan SPLDV

2.       Students are able to solve mathematics models from daily life related with SLETV and its interpretations

Siswa dapat menyelesaikan masalah dari model matematika dari peristiwa sehari-hari yang sesuai dengan SPLDV

Learning Materials :

The Aplication of SLETV

Aplikasi SPLDV

Resume Materials :

4.4. Aplication of  SLETV

1. Mathematical Models
2. Application of SLETV

1.      Mathematical Models

To build the mathematical model, do the following steps :

1. Represent the unknown quantities with distinc variables

Dua besaran yang belum diketahu dimisalkan sebagai variabel dalam SPLDV yang akan dihapus

2. Translate the statements relating the unknown quantities into the mathematical language.

Dua pernyataan yang menghubungkan kedua besaran tersebut diterjemahkan ke dalam kalimat matematika

2.      Application of SLETV

To  solve a SLETV to  word problem related, do the following steps :

1. Build a SLETV for its mathematical models

         Tentukan model matematika menjadi SPLDV

2. Solve the SLETV using one of the available methods

          Selesaikan SPLDV dengan menggunakan salah satu metode

3. Use the root, to answer the questions posed by the problem

          Gunakan solusi SPLDV untuk mencari pertanyaan yang diajukan

Example :

10 books and 4 pencils are sold for Rp. 38.000, while

6 books and 2 pencils are sold for Rp. 22.000.

1. Build its mathematical model involving a system of equation  ?

        Suppose :

                books = x          and        pencils = y

                10 x + 4 y = 38.000

                 6 x + 2 y   = 22.000

2. Determine and solve its system of equations ?

10x + 4y = 38.000  | * 1|  10x + 4y  = 38.000

6x + 2y   = 22.00     | *2|   12x + 4y  = 44.000 –

                                                 - 2x        = - 6.000

                                                     x         = 3.000 

Subtituting  x=31. 000   to                6x + 2y  = 22.000

                                                6 (3.000) +  2y  = 22.000

                                                18.000 + 2y          = 22.000

                                                                  2y       = 4.000

             y              = 2.000

.:.  books (x )   = 3.000                  pencils ( y )    = 2.000 

3. Find the total price 6 pencils and 2 books ?

                 books (x )        = 3.000                  pencils ( y )       = 2.000 

6y + 2 x                 = 6 (2.000) + 2 (3.000)

                                                      = 12.000 +  6.000

      = 18.000

.:. Total price 6 pencils and 2 books are Rp. 18.000

Exercise :

1.       2 pairs of shoes and 3 pairs of slippers are sold Rp. 270.000, while 3 pairs of the same shoes and 4 pairs of the same slippers are sold for Rp 390.000. Find the total price of 4 Pairs of shoes and 5 pairs of slippers!

2.       Two natural numbers adds up to 60 and the differnce between the two is 30. Find that two numbers!

3.       The length of the perimeter of a rectangle is 160 cm. Its length is 20 cm more than its width. Find the length and the width of the rectangle!

4.       4 cows and 3 goats are sold for Rp. 30.400.000 while 2 cows and 5 goats are sold for Rp. 18.000.000. Find the price of cows and goats!

Reference :

•          Adinawan, Cholik. Sugiyono. 2009. Math for Junior High School 1^st  Semester Grade VIII. Jakarta : Erlangga

•          Agus, Nuniek Avianti, 2008. Mudah Belajar Matematika 2 Untuk Kelas VIII SMP/MTs. Jakarta : BSE Departemen Pendidikan Nasional

•          Dirgen Management of Primary and Scondary Education . 2009. Mathematics Grade VIII Junior High School.  Jakarta : Directorate of Junior High School Development

•          Nuharini, Dewi. Tri Wahyuni. 2008. Matematika Konsep dan Aplikasinya Untuk Kelas VIII SMP dan MTs. Jakarta : BSE Departemen Pendidikan Nasional

•          Nugroho,Heru. Lisda Maesaroh. 2009. Matematika SMP  dan MTs Kelas VIII . Jakarta : BSE Departemen Pendidikan Nasional

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Jika mengcopy file ini ke website anda silahkan cantumkan link www.mathematriks.co.cc di website anda , terima kasih

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