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 :
2.2 Solving the mathematics problem of problem which has something to do with SLETV and its estimate.
Menyelesaikan masalah matematika dengan menggunakan Sistem Persamaan Linear Dua Variabel dan perkiraannya.
Learning Objective :
Students are able to determine the root of linear equations system by :
Siswa dapat menentukan penyelesaian dari sistem persamaan linear dengan menggunakan :
1. Substitution
2. Elimination
3. Elimination and Substitution
4. Graphic methods
Learning Materials :
Determining the root of SLETV by :
Menentukan peyelesaian dari SPLDV dengan menggunakan :
1. Substitution
2. Elimination
3. Elimination and Substitution
4. Graphic methods
Resume Materials :
4.2. Solving SLETV
- Substitution Method
- Elimination Method
- Elimination and Subtitution Method
- Graph Method
3. Elimination and Substitution Method
Eliminating and Subtituting means Remove and Replacing
Eliminasi dan Substitusi artinya Menghilangkan dan Mengganti
Method 1 : Eliminating x to find the value of y
Eliminasi x untuk mencari nilai y, kemudian
Subtitution y to find the value of x
Substitusikan y untuk mencari nilai x
Method 2: Eliminating y to find the value of x
Eliminasi y untuk mencari nilai x, kemudian
Subtitution x to find the value of y
Substitusikan x untuk mencari nilai y
Example :
Find the solution to the system of equations consisting of x + y = 6 and 2x – y = 0
Tentukan penyelesaian dari sistem persamaan x + y = 6 dan 2x – y = 0
Method 1 : Eliminating x Subtituting y =4
x + y = 6 | x 2| 2x + 2y = 12 x + y = 6
2x – y = 0 | x 1| 2x – y = 0 -- x + 4 = 6
3y = 12 x = 6 - 4
y = 4 x = 2
.:. The solution is given x = 2 and y = 4
Method 2 : Eliminating y Subtituting x = 2
x + y = 6 | x 1| x + y = 6 x + y = 6
2x – y = 0 | x 1| 2x – y = 0 + 2 + y = 6
3x = 6 y = 6 - 2
x = 2 y = 4
.:. The solution is given x = 2 and y = 4
Exercise :
Find the solution to each of the following systems of equations by Elimination and Subtitution Method
Tentukan penyelesaian sistem persamaan berikut dengan Metode Eliminasi dan Substitusi
- x – y = 3 and 2x + 3y = 16
- 5x + y = 10 and 4x – 2y = -6
- 4x – 5y = - 12 and 2x + 3y = 1
- 2x + 3y – 8 = 0 and 3x + 2y – 7 = 0
- 3x = 2y and 3y = 4x + 1
Reference :
• Adinawan, Cholik. Sugiyono. 2009. Math for Junior High School 1st 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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