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Sistem Persamaan Linear Dua Variabel (SPLDV)

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Sistem Persamaan Linear Dua Variabel (SPLDV)

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Materi SPLDV kelas 8 SMP

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kurikulum65bdg
kurikulum65bdg
Indonesia

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Sistem Persamaan Linear Dua Variabel (SPLDV)
 

Sistem Persamaan Linear Dua Variabel (SPLDV)Online version

Materi SPLDV kelas 8 SMP

by kurikulum65bdg
1

Pengantar SPLDV

SPLDV adalah kumpulan dua persamaan linear dengan dua variabel, misalnya x dan y. Tujuannya menemukan pasangan bilangan yang memenuhi keduanya.

2

Bentuk Umum

Bentuk umum: ax + by = c dan dx + ey = f, dengan a, b, c, d, e, f bilangan nyata. Variabel x dan y adalah tak diketahui.

3

Solusi SPLDV

Solusi SPLDV adalah pasangan bilangan (x, y) yang memenuhi kedua persamaan secara bersamaan. Jika ada, disebut solusi tunggal.

4

Metode Substitusi

Isolasi satu variabel pada salah satu persamaan, lalu substitusi ke persamaan lainnya hingga mendapatkan nilai variabel lainnya.

5

Metode Eliminasi

Penjumlahan atau pengurangan persamaan setelah dikalikan dengan bilangan k untuk mengeliminasi satu variabel, sehingga didapat persamaan linier tunggal.

6

Metode Grafik

Gambarkan setiap persamaan sebagai garis lurus, lalu cari titik potongnya. Titik potong adalah solusi SPLDV jika ada.

7

Langkah Substitusi Contoh

Tada variabel x dari persamaan 1, substitusi ke persamaan 2, selesaikan persamaan satu variabel untuk mendapatkan y, lalu cari x.

8

Contoh Soal

2x + 3y = 12 dan x − y = 1. Substitusi atau eliminasi menunjukkan solusi (x, y) = (3, 1).

9

Penyelesaian Kritis

Jika kedua persamaan sejajar, tidak ada solusi. Jika kedua persamaan sama persis, tak hingga solusi. Pahami kondisi solusi tunggal, tak ada, atau banyak.

10

Latihan Singkat

Solve: 3x + y = 7 dan x + y = 3. Temukan pasangan x dan y yang memenuhi keduanya.
 
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