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The document provides examples and exercises for students to determine systems of linear inequalities from given regions. In the examples, students are shown how to: 1) identify the intersection points with the x- and y-axes to write the equations of lines, 2) test points to write inequalities, and 3) determine the region bounded based on the axes. Students are then given graphs and asked to determine the corresponding systems of inequalities. The goal is for students to understand how to precisely determine systems of linear inequalities from given solution regions by discussing examples in groups.
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2. The notes define key concepts like what makes an equation linear, how to graph linear equations of the form y=mx, y=mx+c, and horizontal and vertical lines. Examples are provided of finding intercepts and using linear equations to check solutions.
3. Practice problems are included for students to complete involving graphing, finding intercepts, determining if ordered pairs are solutions, and matching linear equations to their graphs.
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Bentuk akar
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Lks 2 dikonversi
- 1. A. Tujuan pembelajaran: Peserta didik secara berkelompok memahami dari contoh yang diberikan mengenai cara menentukan sistem pertidaksamaan linear dua variabel dari daerah penyelesaian dengan tepat. B. Perintah: 1. Pahami CONTOH yang diberikan, diskusikan dengan kelompokmu bagaimana cara menentukan sistem pertidaksamaan linear dua variabel dari daerah penyelesaian yang diberikan dalam contoh. 2. Selesaikan SOAL yang disediakan tanpa melihat contoh. Setelah selesai, periksa kembali apakah jawaban sudah sesuai. Jawaban tidak harus ditulis sama persis dengan contoh, boleh disingkat, boleh lebih panjang, boleh menerapkan cara yang berbeda. Pelajari Contoh 1 (5 menit) Daerah yang tidak diarsir (Bersih) pada grafik dibawah merupakan daerah penyelesaian dari suatu sistem pertidaksamaan. Tentukan sistem pertidaksamaan tersebut. LEMBAR KERJA SISWA (LKS)
- 2. Penyelesaian: Langkah 1: Tentukan titik potong dengan sumbu X dan sumbu Y = (2,0) dan (0,4) Langkah 2: Buatlah persamaan garisnya 𝑏𝑥 + 𝑎𝑦 = 𝑎. 𝑏 4𝑥 + 2𝑦 = 4.2 4𝑥 + 2𝑦 = 8 ↔ 2𝑥 + 𝑦 = 4 Langkah 3: Uji titik O (0,0) yang terletak pada daerah penyelesaian = 2(0) + 0 ≤ 4 sehingga diperoleh pertidaksamaan 2𝑥 + 𝑦 ≤ 4 Langkah 4: Daerah yang tidak diarsir (bersih) terletak di: sebelah kanan sumbu Y, maka 𝑥 ≥ 0 sebelah atas sumbu X, maka 𝑦 ≥ 0 Langkah 5: Simpulan Jadi, sistem pertidaksamaannya adalah 2𝑥 + 𝑦 ≤ 4; 𝑥 ≥ 0; 𝑦 ≥ 0; 𝑥, 𝑦 ∈ 𝑹 Pelajari Contoh 2 Daerah yang tidak diarsir (Bersih) pada grafik dibawah merupakan daerah penyelesaian dari suatu sistem pertidaksamaan. Tentukan sistem pertidaksamaan tersebut.
- 3. Penyelesaian: Langkah 1: Tentukan persamaan garis 1 (g1) melalui (4,0) dan (0,4), sehingga persamaannya adalah 4𝑥 + 4𝑦 = 16 ↔ 𝑥 + 𝑦 = 4 Uji titik O (0,0) yang terletak pada daerah penyelesaian, 0 + 0 ≤ 4, sehingga diperoleh 𝑥 + 𝑦 ≤ 4 Langkah 2: Tentukan persamaan garis 1 (g1) melalui (6,0) dan (0,2), sehingga persamaannya adalah 2𝑥 + 6𝑦 = 12 ↔ 𝑥 + 3𝑦 = 6 Uji titik O (0,0) yang terletak pada daerah penyelesaian, 0 + 3(0) ≤ 6, sehingga diperoleh 𝑥 + 3𝑦 ≤ 6 Langkah 3: Daerah yang diarsir terletak di: sebelah kanan sumbu Y, maka 𝑥 ≥ 0 sebelah atas sumbu X, maka 𝑦 ≥ 0 Langkah 4: Simpulan Jadi, sistem pertidaksamaannya adalah 𝑥 + 𝑦 ≤ 4; 𝑥 + 3𝑦 ≤ 6; 𝑥 ≥ 0; 𝑦 ≥ 0; 𝑥, 𝑦 ∈ 𝑹
- 4. Kerjakan soal Soal 1a. Daerah yang tidak diarsir (Bersih) pada grafik dibawah merupakan daerah penyelesaian dari suatu sistem pertidaksamaan. Tentukan sistem pertidaksamaan tersebut. Soal 1b Daerah yang tidak diarsir (Bersih) pada grafik dibawah merupakan daerah penyelesaian dari suatu sistem pertidaksamaan. Tentukan sistem pertidaksamaan tersebut.
- 5. soal 1c Daerah yang tidak diarsir (Bersih) pada grafik dibawah merupakan daerah penyelesaian dari suatu sistem pertidaksamaan. Tentukan sistem pertidaksamaan tersebut. soal 2a Daerah yang tidak diarsir (Bersih) pada grafik dibawah merupakan daerah penyelesaian dari suatu sistem pertidaksamaan. Tentukan sistem pertidaksamaan tersebut.
- 6. soal 2b Daerah yang tidak diarsir (Bersih) pada grafik dibawah merupakan daerah penyelesaian dari suatu sistem pertidaksamaan. Tentukan sistem pertidaksamaan tersebut.