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9.1 GARIS LURUS
Standard pembelajaran 9.1.6
Noor Syamila binti Mohd
STANDARD PEMBELAJARAN:
Menentukan titik persilangan bagi dua garis lurus.
KRITERIA KEJAYAAN:
1. Menyatakan koordinat titik persilangan bagi dua garis lurus
SP 9.1.6
MENENTUKAN TITIK BAGI PERSILANGAN
GARIS LURUS
1. Melukis kedua-dua graf garis lurus
pada satah Cartes yang sama dan
tentukan titik persilangan daripada graf.
2. Penyelesaian persamaan serentak
dengan menggunakan
Titik persilangan bagi dua garis lurus boleh ditentukan dengan kaedah-kaedah berikut:
(a) kaedah
penggantian
(b) kaedah
penghapusan
(A) KAEDAH PENGGANTIAN
Tentukan titik persilangan bagi garis lurus 2𝑥 + 𝑦 = 5 dan garis lurus 𝑥 + 2𝑦 = 1
Contoh 16,m/s 240
penyelesaian
1. Tuliskan persamaan bagi dua garis tersebut.
2. Pilih salah satu persamaan, dan jadikan persamaan
tersebut dengan pekali bagi pemboleh ubah=1
(membentuk persamaan ketiga)
alihkan
3. Gantikan persamaan ke-3 dalam persamaan ke-2
𝑥 + 2(5 – 2𝑥) = 1
Selesaikan, cari nilai pemboleh
ubah
𝑥 + 10 – 4𝑥 = 1
𝑥 – 4𝑥 = 1 – 10
– 3𝑥 = – 9
𝑥 = 3
alihkan
4. Gantikan nilai pemboleh ubah di langkah 3 (𝑥) ke
dalam persamaan ke-3
𝑥 = 3
𝑦 = 5 – 2 3
𝑦 = 5 – 6
𝑦 = – 1
5. Nyatakan titik persilangan (x,y)
𝑥, 𝑦
(3, −1)
1. Tentukan titik persilangan bagi pasangan garis lurus berikut dengan kaedah penggantian.
(d) 2x + y = 3, 3x – 2y = 8
Latihan 9.1h, m/s 244
penyelesaian
1. Tuliskan persamaan bagi dua garis tersebut.
2. Pilih salah satu persamaan, dan jadikan persamaan
tersebut dengan pekali bagi pemboleh ubah=1
(membentuk persamaan ketiga)
3. Gantikan persamaan ke-3 dalam persamaan ke-2
4. Gantikan nilai pemboleh ubah di langkah 3 (𝑥) ke
dalam persamaan ke-3
(A) KAEDAH PENGHAPUSAN
Tentukan titik persilangan bagi garis lurus 2𝑥 + 𝑦 = 5 dan garis lurus 𝑥 + 2𝑦 = 1
Contoh 16,m/s 240
penyelesaian
1. Tuliskan persamaan bagi dua garis tersebut.
2. Pilih pemboleh ubah yang ingin dihapuskan dan
pastikan pekali nya sama. Jika tidak lakukan
pendaraban.
3. Hapuskan pembolehubah tersebut
• Jika pemboleh ubah sama sifat (positif-positif @
negative-negative) : operasi tolak –
• Jika pemboleh ubah berbeza sifat (positif-negatif @
negative-positif) : operasi tambah +
× 2
Samakan pekali
−
/
/
4. Gantikan x = 3 dalam persamaan ke-1
(Cari nilai pembolehubah yang lagi satu)
2𝑥 + 𝑦 = 5
alihkan
5. Nyatakan titik persilangan (x,y)
𝑥, 𝑦
(3, −1)
 m/s 244, 9.1h (soalan 1 dan 2, semua)
KERJA RUMAH

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Bab 9 garis lurus (9.1.6)

  • 1. 9.1 GARIS LURUS Standard pembelajaran 9.1.6 Noor Syamila binti Mohd
  • 2. STANDARD PEMBELAJARAN: Menentukan titik persilangan bagi dua garis lurus. KRITERIA KEJAYAAN: 1. Menyatakan koordinat titik persilangan bagi dua garis lurus SP 9.1.6
  • 3. MENENTUKAN TITIK BAGI PERSILANGAN GARIS LURUS 1. Melukis kedua-dua graf garis lurus pada satah Cartes yang sama dan tentukan titik persilangan daripada graf. 2. Penyelesaian persamaan serentak dengan menggunakan Titik persilangan bagi dua garis lurus boleh ditentukan dengan kaedah-kaedah berikut: (a) kaedah penggantian (b) kaedah penghapusan
  • 4. (A) KAEDAH PENGGANTIAN Tentukan titik persilangan bagi garis lurus 2𝑥 + 𝑦 = 5 dan garis lurus 𝑥 + 2𝑦 = 1 Contoh 16,m/s 240 penyelesaian 1. Tuliskan persamaan bagi dua garis tersebut. 2. Pilih salah satu persamaan, dan jadikan persamaan tersebut dengan pekali bagi pemboleh ubah=1 (membentuk persamaan ketiga) alihkan 3. Gantikan persamaan ke-3 dalam persamaan ke-2 𝑥 + 2(5 – 2𝑥) = 1 Selesaikan, cari nilai pemboleh ubah 𝑥 + 10 – 4𝑥 = 1 𝑥 – 4𝑥 = 1 – 10 – 3𝑥 = – 9 𝑥 = 3 alihkan
  • 5. 4. Gantikan nilai pemboleh ubah di langkah 3 (𝑥) ke dalam persamaan ke-3 𝑥 = 3 𝑦 = 5 – 2 3 𝑦 = 5 – 6 𝑦 = – 1 5. Nyatakan titik persilangan (x,y) 𝑥, 𝑦 (3, −1)
  • 6. 1. Tentukan titik persilangan bagi pasangan garis lurus berikut dengan kaedah penggantian. (d) 2x + y = 3, 3x – 2y = 8 Latihan 9.1h, m/s 244 penyelesaian 1. Tuliskan persamaan bagi dua garis tersebut. 2. Pilih salah satu persamaan, dan jadikan persamaan tersebut dengan pekali bagi pemboleh ubah=1 (membentuk persamaan ketiga) 3. Gantikan persamaan ke-3 dalam persamaan ke-2
  • 7. 4. Gantikan nilai pemboleh ubah di langkah 3 (𝑥) ke dalam persamaan ke-3
  • 8. (A) KAEDAH PENGHAPUSAN Tentukan titik persilangan bagi garis lurus 2𝑥 + 𝑦 = 5 dan garis lurus 𝑥 + 2𝑦 = 1 Contoh 16,m/s 240 penyelesaian 1. Tuliskan persamaan bagi dua garis tersebut. 2. Pilih pemboleh ubah yang ingin dihapuskan dan pastikan pekali nya sama. Jika tidak lakukan pendaraban. 3. Hapuskan pembolehubah tersebut • Jika pemboleh ubah sama sifat (positif-positif @ negative-negative) : operasi tolak – • Jika pemboleh ubah berbeza sifat (positif-negatif @ negative-positif) : operasi tambah + × 2 Samakan pekali − / /
  • 9. 4. Gantikan x = 3 dalam persamaan ke-1 (Cari nilai pembolehubah yang lagi satu) 2𝑥 + 𝑦 = 5 alihkan 5. Nyatakan titik persilangan (x,y) 𝑥, 𝑦 (3, −1)
  • 10.  m/s 244, 9.1h (soalan 1 dan 2, semua) KERJA RUMAH