Grade 8 - Chapter 4 - SLETV/SPLDV Part 1

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 :

2.1. Solve System of Linear Equations in Two Variables (SLETV)

Menyelesaikan Sistem Persamaan Linear Dua Variable

Learning Objective :

1.         Students are able to mention the differences between linear equation with two variables (LETV) and system of linear equations in two variables (SLETV)

Siswa mengetahui perbedaan antara Persamaan Linear Dua Variable (PLDV) dan System Persamaan Linear Dua Variable (SPLDV)

2.         Students are understand the meaning of root

Siswa mengetahui cara mendapatkan solusi dari SPLDV

3.         Students are able to know linear equations system in various form and variables

Siswa dapat mengetahui sistem persamaan linear dalam berbagai bentuk dan variabel

Learning Materials :

1.         Systems of Linear Equations in Two Variables (SLETV)

System Persamaan Linear Dua Variable (SPLDV)

2.         The definition of SLETV, LETV, and the root of LETV

Devinisi SPLDV, PLDV dan solusi dari PLDV

Resume Materials :

4.1. LETV and SLETV

1. Linear Equations in One Variables (LEOV)

Persamaan Linear Satu Variable (PLSV)

2. Linear Equations in Two Variables (LETV)

Persamaan Linear Dua Variable (PLDV)

3. System of Linear Equations in Two Variables (SLETV)

System Persamaan Linear Dua Variable (SPLDV)

4. Difference between LETV and SLETV

Perbedaan antara PLDV dan SPLDV

1. Linear Equations in One Variables (LEOV)

Persamaan Liniar Satu Variabel (PLSV)

Equations in one variables with the variable being to its first power are called linear equations in one variable.

Persamaan yang memiliki satu variabel dan variabelnya berpangkat satu disebut persamaan linear satu variabel

Example :

1. a + 5 = 7               variable : a
2. 3p – 2 = 13           variable                : p
3. x = 3x + 6             variable                : x

2. Linear Equations in Two Variables (LETV)

Persamaan Liniar Dua Variabel (PLSV)

Equations involves two variable is raised to its first power are called linear equations in two variable.

Persamaan yang memiliki dua variabel dan variabelnya berpangkat satu disebut persamaan linear dua variabel

Example :

1. x + y = 4                                variable : x and y
2. 2p – 3q + 12 = 0                 variable                : p and q
3. q = 2p -4                               variable                : p and q

3. System of Linear Equations  in Two Variables  (SLETV)

System Persamaan Liniar Dua Variabel (SPLDV)

A system of linear equations in two variables (SLETV)  x and y is written as :

Sistem Persamaan Linier Dua Variabel (SPLDV) x dan y dapat dinyatakan dengan :

          a1x + b1y = c1    and        a2x + b2y = c2

Where a1, a2, b1, and b2 are real number.

Dengan a1, a2, b1 dan b2 adalah bilangan asli

Example :

A SLETV can be expressed in any of two following ways :

SPLDV dapat dinyatakan dalam dua bentuk seperti berikut :

1. x + y = 5 and 2x – y = 4

2.      

 4. Difference between LETV and SLETV

Perbedaan PLDV dan SPLDV

On solving LETV has a infinite number solution

PLDV mempunyai penyelesaian yang tak terhingga banyaknya.

Example        :

                x+ y = 7

The equations x + y = 7 has a infinite number of solutions, among others :

Persamaan x + y = 7 mempunyai penyelesaian yang terhingga, seperti :

                x= 0        and        y = 7

                x = 1       and        y = 6

                x = 3       and        y = 4      

                etc

While a SLETV consisting of two related LETVs has one or more solutions which must simultaneously satisfy both LETVs.

Sedangkan SPLDV terdiri dari dua PLDV yang saling berkait dalam hal penyelesaiannya, sehingga kedua penyelesaian harus memenuhi kedua PLDV pembentuknya.

Example :

                x+ 2y = 8              and        2x + 3y =13

The two equations have a commont solution. i.e x =2 and y = 3, Subtituting  x=2 and y= 3.

Dua persamaan akan mempunyai solusi berupa x =2 dan y = 3, bukti :

                x + 2y = 2 + 2 (3)                = 8

                2x + y = 2 (2) + 3 (3)         = 13

Exercise :

1.       Find the solution or root of each of the following equation! (find 4 solution at most)

Tentukan penyelesaian dari persamaan berikut (maksimal 4 penyelesaian)

a.      x + y =9

b.      4x + 2y = 20

c.       3x – y = 10

2.       Which the following systems of linear equations in two variables have p =2 and q = 4 as their solution?

Diantara SPLDV berikut, manakah yang mempunyai penyelesaian p = 2 dan q =4

a.      p + q = 6 and p – q = -2

b.      2p + q = 8 and p + 2q = 10

c.       2p – q = 0 and 3p + 2q = 12

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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