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Sistem Persamaan 2 Linear

FKIP-UNA

manakala
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Sistem Persamaan 2 Linear

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  1. SISTEM PERSAMAAN By : Novita Sari FKIP UNA

  2. APAKAH YANG DIMAKSUD DENGAN PERSAMAAN ?

  3. PERSAMAAN IALAH KALIMAT TERBUKA YANG MENYATAKAN HUBUNGAN SAMA DENGAN.

  4. 1. Sistem Persamaan Linear • SistemPersamaan Linear DuaVariabel Bentukumum : Keterangan : a = koefisien x b = koefisien y x,y = variabel ( peubah ) ax + by = c

  5. Pasanganbilanganpengganti x dan y dalambentukhimpunandisebutHimpunanPenyelesaian ( HP ). Menyelesaikansistempersamaan linear duapeubah, denganmenggunakanmetodegrafikdanaljabar ( subsitusidangabunganeliminasidansubsitusi )

  6. ContohMetodeSubsitusi

  7. Tentukan Hp sistem persamaan linear dua variabel berikut : 2x + y = 5 3x – 2 y = 4

  8. PENYELESAIAN :

  9. Dari persamaan 2x + y = 5 dapat dibentuk y = 5 – 2x. Kemudian dari persamaan y = 5 – 2x dimasukkan kedalam persamaan 3x – 2y = 4 2x + y = 5 3x – 2 y = 4

  10. 3x – 2y = 4 • 3x – 2 ( 5 – 2x ) = 4 • 3x – 10 + 4x = 4 • 3x + 4x = 4 + 10 • 7 x = 14 • x = 2 Hasil X = 2 dimasukkandalampersamaan 2x + y = 5 • 2x + y = 5 • 2(2) + y = 5 • 4 + y = 5 • y = 5 - 4 • y = • Jadi, Hp = { 2, 1 }

  11. Metode Gabungan Eliminasi Dan Subsitusi

  12. Tentukan himpunan penyelesaian dari 2x - 3y = 7………………(1) 3x – 2 y = 4………………(2)

  13. PENYELESAIAN :

  14. Langkah 1 ( Eliminasi ) Menghilangkansalahsatuvariabel 2x -3 y = 7 x 1 2x – 3y = 7 3x + y = 6 x 3 9x + 3y = 18 + 11x = 25 x = 25/11

  15. Langkah 2 ( Subsitusi ) Subsitusikan x = 25/11 kepersamaan (1) yaitu : 2(25/11) – 3y = 7 • 3y = 50/11 – 7 • 3y = - 27/11 • y = - 9/11 • Jadi, Hp = { 25/11, -9/11 }

  16. SOAL • Himpunanpenyelesaiandari 3x – 2y = 8 dan 2x + 5y = -1 adalah…….. • Himpunanpenyelesaian 3x – y + 4 = 0 dengan x ∈ { 0,1,2,3,4 } dan y bilanganbulatadalah…….. • Himpunanpenyelesaiandari 2x + 2y = 48 dan x – y = 6 adalah….

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