Pada artikel Matematika kelas 8 kali ini, kamu akan mempelajari tentang cara menyelesaikan Sistem Persamaan Linear Dua Variabel (SPLDV) dan contoh soalnya. Ada metode grafik, metode substitudi, metode eliminasi, dan metode campuran.
—
Tu, wa, yah malah nyangkut! (sumber: giphy.com)
Lihat! Ada yang sedang berolahraga! Kumamon si maskot beruang lucu asal Jepang ini sepertinya ingin melakukan lompat tali, ya. Tapi, sayangnya, tali yang digunakan terlalu pendek, nih. Jadi, nyangkut deh di tubuh gembulnya Kumamon.
Kamu tahu nggak, nih. Ternyata, masalah Kumamon ini bisa diselesaikan dengan menggunakan Matematika, lho, yaitu dengan penyelesaian Sistem Persamaan Linear Dua Variabel (SPLDV). Nah, untuk menyelesaikan masalah dengan menggunakan SPLDV ini, kita harus melewati langkah-langkahnya dulu. Jadi, nggak bisa asal-asalan dalam menentukan solusinya.
Mau tahu apa saja langkah-langkahnya? Yuk, simak penjelasannya pada artikel berikut ini!
Mengenal Sistem Persamaan Linear Dua Variabel (SPLDV)
Oh iya, sebelum itu, kita ketahui dulu yuk, apa itu SPLDV. Di kelas 7, tentunya, kamu sudah mempelajari materi tentang Persamaan Linear Satu Variabel (PLSV), ya. Selain ada PLSV, ada juga yang namanya Persamaan Linear Dua Variabel (PLDV), nih.
Lalu, apa sih bedanya PLSV dengan PLDV? Bedanya, kalau PLSV, persamaannya hanya memiliki satu variabel saja, sedangkan PLDV, persamaannya memiliki dua variabel. Nah, variabel-variabel ini hanya memiliki pangkat atau derajat bernilai satu. Kamu bingung nggak, nih? Kalau bingung, yuk, coba perhatikan perbedaan contoh PLSV dan PLDV di bawah ini!
Baca Juga: Bagaimana Cara Menentukan Persamaan Garis Lurus?
Bentuk Umum Sistem Persamaan Linear Dua Variabel (SPLDV)
Bagaimana, sudah paham kan letak perbedaannya? Apabila terdapat dua atau lebih PLDV yang memiliki hubungan satu sama lain dan memiliki satu buah penyelesaian, maka itulah yang dinamakan dengan SPLDV. Bentuk umum SPLDV adalah sebagai berikut:
SPLDV ini biasanya digunakan untuk menyelesaikan masalah sehari-hari yang membutuhkan penggunaan Matematika, seperti menentukan harga suatu barang, mencari keuntungan penjualan, sampai menentukan ukuran suatu benda seperti masalah Kumamon di atas, lho.
Langkah-Langkah untuk Menyelesaikan Masalah dengan SPLDV
Oh iya, seperti yang sudah dituliskan sebelumnya, terdapat langkah-langkah tertentu untuk menyelesaikan masalah dengan menggunakan SPLDV, yaitu:
-
Mengganti setiap besaran yang ada di masalah tersebut dengan variabel (biasanya dilambangkan dengan huruf atau simbol).
-
Membuat model Matematika dari masalah tersebut. Model Matematika ini dirumuskan mengikuti bentuk umum SPLDV.
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Mencari solusi dari model permasalahan tersebut dengan menggunakan metode penyelesaian SPLDV.
Nah, karena kamu sudah tahu apa saja langkah-langkahnya, sekarang, ayo kita bantu selesaikan masalah Kumamon!
Penyelesaian:
Langkah pertama yang harus kita lakukan adalah mengganti semua besaran yang ada di dalam soal dengan variabel. Kita misalkan:
x = panjang tali (dalam cm) dan y = tinggi badan (dalam cm)
Lalu, kita buat model Matematika dari permasalahan tersebut.
Panjang tali 70 cm lebih pendek dari tinggi Kumamon → x = y – 70 atau -x + y = 70
Dua kali panjang tali 30 cm lebih panjang dari tinggi Kumamon → 2x = 30 + y atau 2x – y = 30
Sehingga, diperoleh model Matematika-nya sebagai berikut:
Persamaan I: -x + y = 70
Persamaan II: 2x – y = 30
Sampai di sini kamu paham, kan? Nah, langkah selanjutnya, kita akan mencari nilai x dan y sebagai solusi dari masalah di atas dengan menggunakan metode penyelesaian SPLDV. Ternyata, metode penyelesaian SPLDV ini nggak hanya satu saja, melainkan ada empat macam metode penyelesaian yang akan dibahas di bawah ini. So, simak terus, ya!
Baca Juga: Perbedaan Persamaan dan Pertidaksamaan Linear
Metode Penyelesaian Sistem Persamaan Linear Dua Variabel (SPLDV)
Terdapat 4 metode yang dapat digunakan untuk menyelesaikan SPLDV, di antaranya metode grafik, metode eliminasi, metode substitusi, dan metode campuran. Yuk, simak masing-masing penjelasannya disertai contoh soal!
1. Metode Grafik
Pada metode grafik, kita akan menggambar grafik dari dua buah persamaan yang telah kita buat pada langkah sebelumnya. Cara yang paling mudah untuk menggambar grafik adalah dengan mencari titik potong terhadap sumbu x dan sumbu y. Berdasarkan contoh di atas, kita dapat menentukan titik potong dari masing-masing persamaan sebagai berikut:
Contoh soal dan penyelesaian SPLDV menggunakan metode grafik:
Sehingga, diperoleh titik potong dari kedua garis yaitu (x,y) = (100,170). Sebelumnya, kita telah memisalkan panjang tali dengan variabel x dan tinggi Kumamon dengan variabel y. Jadi, sudah dapat ditentukan nih berapa panjang tali dan juga tinggi si Kumamon itu. Yap! Jawabannya adalah 100 cm untuk panjang tali dan 170 cm untuk tinggi Kumamon.
Bagaimana, mudah, kan? Metode grafik ini biasanya berguna jika nilai koefisien dan nilai konstanta dari persamaannya bukan merupakan bilangan bulat, sehingga lebih baik digambar untuk memudahkan mencari nilai x dan y nya.
2. Metode Eliminasi
Metode yang kedua adalah metode eliminasi. Metode ini bertujuan untuk mengeliminasi (menghilangkan) salah satu variabel, sehingga nilai variabel lainnya bisa diketahui. Caranya dapat kamu lihat pada contoh di bawah ini.
Contoh soal dan penyelesaian SPLDV menggunakan metode eliminasi:
Berdasarkan metode eliminasi, diperoleh nilai x = 100 dan y = 170. Jadi, dapat diketahui kalau panjang tali adalah 100 cm dan tinggi badan Kumamon adalah 170 cm. Sampai sini, menurut kamu, lebih mudah pakai metode yang mana, nih? Hehe…
Baca Juga: Sistem Koordinat Kartesius dan Cara Membuat Grafiknya
3. Metode Substitusi
Metode substitusi bertujuan untuk mengganti nilai suatu variabel pada suatu persamaan dari persamaan lainnya. Hah?! Gimana, gimana? Tenang, kalau bingung, caranya dapat kamu lihat ada contoh berikut ini:
Contoh soal dan penyelesaian SPLDV menggunakan metode substitusi:
Berdasarkan metode substitusi, diperoleh nilai x = 100 dan y = 170. Jadi, dapat diketahui kalau tinggi badan Kumamon adalah sebesar 170 cm dan tali yang dipakai Kumamon untuk bermain lompat tali adalah 100 cm.
4. Metode Campuran (Gabungan)
Metode ini merupakan gabungan dari metode eliminasi dan substitusi. Caranya, kamu dapat menggunakan metode eliminasi untuk mencari nilai x terlebih dahulu, kemudian ganti variabel x dengan nilai x yang sudah diperoleh dengan menggunakan metode substitusi untuk memperoleh nilai y. Atau sebaliknya, ya. Paham, nggak? Yuk, kita simak baik-baik caranya pada contoh di bawah ini!
Contoh soal dan penyelesaian SPLDV menggunakan metode gabungan:
Berdasarkan metode gabungan, diperoleh nilai x = 100 dan y = 170. Sehingga, dapat diketahui kalau panjang tali adalah sebesar 100 cm dan tinggi Kumamon adalah 170 cm. Perlu kamu ketahui kalau metode gabungan ini merupakan metode yang paling banyak dipakai untuk menyelesaikan masalah SPLDV.
Nah, kalau kamu perhatikan, dari keempat metode penyelesaian SPLDV di atas, akan diperoleh hasil yang sama. Jadi, bebas sebenarnya mau pakai metode yang mana saja. Meskipun begitu, kamu harus tetap menguasai keempat-empatnya, ya.
Selanjutnya, kita akan mencari tahu berapa panjang tali yang diperlukan agar Kumamon dapat bermain lompat tali tanpa harus tersangkut di tubuh gemoynya. Jika kamu membaca kembali contoh soal di atas, maka dapat diketahui kalau setidaknya, tali tersebut harus dua kali lebih panjang dari ukuran sebelumnya (2x). Jadi, sudah dapat kita ketahui ya, kalau panjang tali yang diperlukan agar tidak tersangkut di tubuh gemoy Kumamon adalah 2x = 2(100) = 200 cm.
Baca Juga: Cara Mencari Kemiringan (Gradien) pada Garis Lurus
Oke, apa tanggapanmu setelah mempelajari keempat metode penyelesaian SPLDV di atas? Easy bukan? Meskipun kelihatannya panjang dan rumit, tapi jika kamu memperbanyak latihan soal, pasti akan mudah, kok.
Oh iya, bagi kamu yang masih bingung dengan materi ini, jangan ragu untuk tuliskan pertanyaanmu di kolom komentar, ya. Kamu juga bisa lho mempelajari materi ini dalam bentuk video menarik bareng Master Teacher yang asik lewat ruangbelajar. Belajar jadi mudah dan pastinya banyak latihan soal yang bikin kamu antiremed!
Referensi:
As’ari A.R, Tohir M, Valentino E, Imron Z, Taufiq I. (2017) Matematika SMP/MTs Kelas VIII Semester 1. Jakarta: Kementerian Pendidikan dan Kebudayaan
Sumber foto:
GIF ‘Kumamon Loncat’ [Daring]. Tautan: https://giphy.com/gifs/kumamon-LVWzUCdGioDBe (Diakses: 23 Desember 2020)
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<h1 class="content-title">
Cara Menyelesaikan Sistem Persamaan Linear Dua Variabel (SPLDV) | Matematika Kelas 8 </h1>
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<p class="content-author"><a href="https://www.ruangguru.com/blog/author/hani-ammariah" class="">Hani Ammariah</a> </p>
<p class="content-info"><span>September 12, 2024 • </span> <span>6 minutes read</span></p>
<br />
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<p><img decoding="async" style="width: 820px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/08MAT%20-%20Sistem%20Persamaan%20Linear%20Dua%20Variabel-01.jpg" alt="Sistem Persamaan Linear Dua Variabel" width="820" /></p>
<blockquote>
<p style="text-align: center;"><em>Pada <strong><a href="https://www.ruangguru.com/blog/c/matematika/matematika-smp-kelas-8">artikel Matematika kelas 8</a></strong> kali ini, kamu akan mempelajari tentang cara menyelesaikan Sistem Persamaan Linear Dua Variabel (SPLDV) dan contoh soalnya. Ada metode grafik, metode substitudi, metode eliminasi, dan metode campuran.</em></p>
</blockquote>
<p style="text-align: center;"><em>—</em></p>
<p> </p>
<p><img decoding="async" style="width: 396px; display: block; margin: 0px auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Kumamon%20loncat.gif" alt="Kumamon" width="396" /></p>
<p style="text-align: center;"><em><span style="background-color: transparent;">Tu, wa, yah malah nyangkut! (sumber: giphy.com)</span></em></p>
<p> </p>
<p style="text-align: justify;">Lihat! Ada yang sedang berolahraga! Kumamon si maskot beruang lucu asal Jepang ini sepertinya ingin melakukan lompat tali, ya. Tapi, sayangnya, tali yang digunakan terlalu pendek, <em>nih</em>. Jadi, <em>nyangkut deh</em> di tubuh gembulnya Kumamon.</p>
<p style="text-align: justify;">Kamu tahu <em>nggak</em>, <em>nih</em>. Ternyata, masalah Kumamon ini bisa diselesaikan dengan menggunakan Matematika, <em>lho</em>, yaitu dengan penyelesaian Sistem Persamaan Linear Dua Variabel (SPLDV). <em>Nah</em>, untuk menyelesaikan masalah dengan menggunakan SPLDV ini, kita harus melewati langkah-langkahnya dulu. Jadi, <em>nggak</em> bisa asal-asalan dalam menentukan solusinya.</p>
<p style="text-align: justify;">Mau tahu apa saja langkah-langkahnya? <em>Yuk</em>, simak penjelasannya pada artikel berikut ini!</p>
<p> </p>
<h2 style="text-align: justify;"><span style="font-size: 18pt;">Mengenal Sistem Persamaan Linear Dua Variabel (SPLDV)</span></h2>
<p style="text-align: justify;">Oh iya, sebelum itu, kita ketahui dulu <span style="font-style: italic;">yuk</span>, apa itu SPLDV. Di kelas 7, tentunya, kamu sudah mempelajari materi tentang <strong><a href="/blog/sistem-persamaan-linear-satu-variabel-splsv" rel="noopener">Persamaan Linear Satu Variabel (PLSV)</a></strong>, ya. Selain ada PLSV, ada juga yang namanya Persamaan Linear Dua Variabel (PLDV), <span style="font-style: italic;">nih</span>.</p>
<p style="text-align: justify;">Lalu, apa <em>sih</em> bedanya PLSV dengan PLDV? Bedanya, kalau <strong>PLSV</strong>, persamaannya hanya memiliki <strong>satu variabel saja</strong>, sedangkan <strong>PLDV</strong>, persamaannya memiliki <strong>dua variabel</strong>. <em>Nah</em>, variabel-variabel ini hanya memiliki <strong>pangkat atau derajat bernilai satu</strong>. Kamu bingung <em>nggak</em>, <em>nih</em>? Kalau bingung, y<em>uk</em>, coba perhatikan perbedaan contoh PLSV dan PLDV di bawah ini!<span style="background-color: transparent;"> </span></p>
<p><img decoding="async" class="aligncenter" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/08MAT%20-%20Sistem%20Persamaan%20Linear%20Dua%20Variabel-03.jpg" alt="bentuk persamaan linear" width="600" /><br />
<strong>Baca Juga: <a href="https://www.ruangguru.com/blog/matematika-kelas-8-cara-menentukan-persamaan-garis-lurus">Bagaimana Cara Menentukan Persamaan Garis Lurus?</a></strong></p>
<p> </p>
<h2 style="text-align: justify;"><span style="font-size: 18pt;">Bentuk Umum Sistem Persamaan Linear Dua Variabel (SPLDV)</span></h2>
<p style="text-align: justify;">Bagaimana, sudah paham <em>kan</em> letak perbedaannya? Apabila terdapat dua atau lebih <strong>PLDV yang memiliki hubungan satu sama lain dan memiliki satu buah penyelesaian</strong>, maka itulah yang dinamakan dengan <strong>SPLDV</strong>. Bentuk umum SPLDV adalah sebagai berikut:</p>
<p><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/08MAT%20-%20Sistem%20Persamaan%20Linear%20Dua%20Variabel-04.jpg" alt="bentuk persamaan linear dua variabel" /></p>
<p> </p>
<p style="text-align: justify;"><strong>SPLDV</strong> ini biasanya <strong>digunakan untuk menyelesaikan masalah sehari-hari</strong> yang membutuhkan penggunaan Matematika, seperti menentukan harga suatu barang, mencari keuntungan penjualan, sampai menentukan ukuran suatu benda seperti masalah Kumamon di atas, <em>lho</em>.</p>
<p> </p>
<h2 style="text-align: justify;"><span style="font-size: 18pt;">Langkah-Langkah untuk Menyelesaikan Masalah dengan SPLDV</span></h2>
<p style="text-align: justify;">Oh iya, seperti yang sudah dituliskan sebelumnya, terdapat <strong>langkah-langkah</strong> <strong>tertentu untuk menyelesaikan masalah dengan menggunakan SPLDV</strong>, yaitu:</p>
<ol style="text-align: justify;">
<li><strong>Mengganti setiap besaran</strong> yang ada di masalah tersebut <strong>dengan variabel</strong> (biasanya dilambangkan dengan huruf atau simbol).</li>
<li><strong>Membuat model Matematika</strong> dari masalah tersebut. Model Matematika ini dirumuskan mengikuti bentuk umum SPLDV.</li>
<li><strong>Mencari solusi</strong> dari model permasalahan tersebut dengan menggunakan metode penyelesaian SPLDV.</li>
</ol>
<p> </p>
<p style="text-align: justify;"><em>Nah</em>, karena kamu sudah tahu apa saja langkah-langkahnya, sekarang, ayo kita bantu selesaikan masalah Kumamon!</p>
<p><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/08MAT%20-%20Sistem%20Persamaan%20Linear%20Dua%20Variabel-05.jpg" alt="contoh soal persamaan linear dua variabel" width="600" /></p>
<p> </p>
<p><strong>Penyelesaian:</strong></p>
<p style="text-align: justify;"><span style="background-color: transparent; font-size: 1rem; text-align: left;">Langkah pertama yang harus kita lakukan adalah mengganti semua besaran yang ada di dalam soal dengan variabel. Kita misalkan:</span></p>
<p style="text-align: justify;">x = panjang tali (dalam cm) dan y = tinggi badan (dalam cm)</p>
<p style="text-align: justify;"><span style="background-color: transparent; font-size: 1rem; text-align: left;">Lalu, kita buat model Matematika dari permasalahan tersebut.</span></p>
<p style="text-align: justify;">Panjang tali 70 cm lebih pendek dari tinggi Kumamon → x = y – 70 atau -x + y = 70</p>
<p style="text-align: justify;">Dua kali panjang tali 30 cm lebih panjang dari tinggi Kumamon → 2x = 30 + y atau 2x – y = 30</p>
<p style="text-align: justify;">Sehingga, diperoleh model Matematika-nya sebagai berikut:</p>
<p style="text-align: justify;"><strong>Persamaan I</strong>: -x + y = 70</p>
<p style="text-align: justify;"><strong>Persamaan II</strong>: 2x – y = 30</p>
<p style="text-align: justify;">Sampai di sini kamu paham, <em>kan</em>? <em>Nah</em>, langkah selanjutnya, kita akan mencari nilai x dan y sebagai solusi dari masalah di atas dengan menggunakan metode penyelesaian SPLDV. Ternyata, metode penyelesaian SPLDV ini <em>nggak</em> hanya satu saja, melainkan ada empat macam metode penyelesaian yang akan dibahas di bawah ini. <em>So</em>, simak terus, ya!</p>
<p><strong>Baca Juga: <a href="https://www.ruangguru.com/blog/perbedaan-persamaan-linear-dan-pertidaksamaan-linear">Perbedaan Persamaan dan Pertidaksamaan Linear</a></strong></p>
<p> </p>
<h2><span style="font-size: 18pt;">Metode Penyelesaian Sistem Persamaan Linear Dua Variabel (SPLDV)</span></h2>
<p style="text-align: justify;">Terdapat 4 metode yang dapat digunakan untuk menyelesaikan SPLDV, di antaranya metode grafik, metode eliminasi, metode substitusi, dan metode campuran. Yuk, simak masing-masing penjelasannya disertai contoh soal!</p>
<p> </p>
<h3><span style="font-size: 14pt;">1. Metode Grafik</span></h3>
<p style="text-align: justify;">Pada metode grafik, kita akan menggambar grafik dari dua buah persamaan yang telah kita buat pada langkah sebelumnya. Cara yang paling mudah untuk menggambar grafik adalah dengan <strong>mencari titik potong terhadap sumbu x dan sumbu y</strong>. Berdasarkan contoh di atas, kita dapat menentukan titik potong dari masing-masing persamaan sebagai berikut:</p>
<p><strong>Contoh soal dan penyelesaian SPLDV menggunakan metode grafik:</strong></p>
<p><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/08MAT%20-%20Sistem%20Persamaan%20Linear%20Dua%20Variabel-06.jpg" alt="metode grafik spldv" width="600" /></p>
<p> </p>
<p style="text-align: justify;">Sehingga, diperoleh titik potong dari kedua garis yaitu (x,y) = (100,170). Sebelumnya, kita telah memisalkan panjang tali dengan variabel x dan tinggi Kumamon dengan variabel y. Jadi, sudah dapat ditentukan <em>nih</em> berapa panjang tali dan juga tinggi si Kumamon itu. <em>Yap</em>! <strong>Jawabannya adalah 100 cm untuk panjang tali dan 170 cm untuk tinggi Kumamon</strong>.</p>
<p style="text-align: justify;">Bagaimana, mudah, <em>kan</em>? <strong>Metode grafik</strong> ini biasanya <strong>berguna jika nilai koefisien dan nilai konstanta dari persamaannya bukan merupakan bilangan bulat</strong>, sehingga lebih baik digambar untuk memudahkan mencari nilai x dan y nya.</p>
<p> </p>
<h3><span style="font-size: 14pt;">2. Metode Eliminasi</span></h3>
<p style="text-align: justify;">Metode yang kedua adalah metode eliminasi. Metode ini bertujuan untuk <span style="font-weight: bold;">mengeliminasi (menghilangkan)</span> salah satu variabel, sehingga nilai variabel lainnya bisa diketahui. Caranya dapat kamu lihat pada contoh di bawah ini.</p>
<p><strong>Contoh soal dan penyelesaian SPLDV menggunakan metode eliminasi:</strong></p>
<p><img decoding="async" class="aligncenter size-medium" src="https://cdn-web-2.ruangguru.com/landing-pages/assets/c6549777-de89-4042-adfe-f1323382f336.png" alt="metode eliminasi - spldv - matematika kelas 8" /></p>
<p> </p>
<p style="text-align: justify;">Berdasarkan metode eliminasi, diperoleh nilai x = 100 dan y = 170. Jadi, dapat diketahui kalau <strong>panjang tali adalah 100 cm dan tinggi badan Kumamon adalah 170 cm</strong>. Sampai sini, menurut kamu, lebih mudah pakai metode yang mana, <em>nih</em>? <em>Hehe</em>…</p>
<p><strong>Baca Juga: <a href="https://www.ruangguru.com/blog/sistem-koordinat-kartesius-dan-cara-membuat-grafiknya-matematika-kelas-8">Sistem Koordinat Kartesius dan Cara Membuat Grafiknya</a></strong></p>
<p> </p>
<h3><span style="font-size: 14pt;">3. Metode Substitusi</span></h3>
<p style="text-align: justify;">Metode substitusi bertujuan untuk <strong>mengganti nilai suatu variabel pada suatu persamaan dari persamaan lainnya. </strong>Hah?! Gimana, gimana? Tenang, kalau bingung, caranya dapat kamu lihat ada contoh berikut ini:</p>
<p><strong>Contoh soal dan penyelesaian SPLDV menggunakan metode substitusi:</strong></p>
<p><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/08MAT%20-%20Sistem%20Persamaan%20Linear%20Dua%20Variabel-08.jpg" alt="metode substitusi spldv" width="600" /></p>
<p> </p>
<p style="text-align: justify;">Berdasarkan metode substitusi, diperoleh nilai x = 100 dan y = 170. Jadi, dapat diketahui kalau <strong>tinggi badan Kumamon adalah sebesar 170 cm dan tali yang dipakai Kumamon untuk bermain lompat tali adalah 100 cm</strong>.</p>
<p> </p>
<h3><span style="font-size: 14pt;">4. Metode Campuran (Gabungan)</span></h3>
<p style="text-align: justify;">Metode ini merupakan <strong>gabungan dari metode eliminasi dan substitusi</strong>. Caranya, kamu dapat menggunakan metode eliminasi untuk mencari nilai x terlebih dahulu, kemudian ganti variabel x dengan nilai x yang sudah diperoleh dengan menggunakan metode substitusi untuk memperoleh nilai y. Atau sebaliknya, ya. Paham, <em>nggak</em>? <em>Yuk</em>, kita simak baik-baik caranya pada contoh di bawah ini!</p>
<p><strong>Contoh soal dan penyelesaian SPLDV menggunakan metode gabungan:</strong></p>
<p><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/08MAT%20-%20Sistem%20Persamaan%20Linear%20Dua%20Variabel-09.jpg" alt="metode gabungan spldv" width="600" /></p>
<p> </p>
<p style="text-align: justify;">Berdasarkan metode gabungan, diperoleh nilai x = 100 dan y = 170. Sehingga, dapat diketahui kalau <strong>panjang tali adalah sebesar 100 cm dan tinggi Kumamon adalah 170 cm</strong>. Perlu kamu ketahui kalau <strong>metode gabungan</strong> ini merupakan <strong>metode yang paling banyak dipakai untuk menyelesaikan masalah SPLDV</strong>.</p>
<p style="text-align: justify;"><em>Nah</em>, kalau kamu perhatikan, dari keempat metode penyelesaian SPLDV di atas, akan diperoleh hasil yang sama. Jadi, bebas sebenarnya mau pakai metode yang mana saja. Meskipun begitu, kamu harus tetap menguasai keempat-empatnya, ya.</p>
<p style="text-align: justify;">Selanjutnya, kita akan mencari tahu berapa panjang tali yang diperlukan agar Kumamon dapat bermain lompat tali tanpa harus tersangkut di tubuh <em>gemoynya</em>. Jika kamu membaca kembali contoh soal di atas, maka dapat diketahui kalau setidaknya, tali tersebut harus <strong>dua kali lebih panjang</strong> dari ukuran sebelumnya (2x). Jadi, sudah dapat kita ketahui ya, kalau <strong>panjang tali yang diperlukan agar tidak tersangkut di tubuh <em>gemoy</em> Kumamon adalah 2x = 2(100) = 200 cm</strong>.</p>
<p><strong>Baca Juga: <a href="/blog/matematika-kelas-8-3-cara-mencari-kemiringan-garis-lurus" rel="noopener">Cara Mencari Kemiringan (Gradien) pada Garis Lurus</a></strong></p>
<p style="text-align: justify;">Oke, apa tanggapanmu setelah mempelajari keempat metode penyelesaian SPLDV di atas? <em>Easy</em> bukan? Meskipun kelihatannya panjang dan rumit, tapi jika kamu memperbanyak latihan soal, pasti akan mudah, <em>kok</em>.</p>
<p style="text-align: justify;">Oh iya, bagi kamu yang masih bingung dengan materi ini, jangan ragu untuk tuliskan pertanyaanmu di kolom komentar, ya. Kamu juga bisa <em>lho</em> mempelajari materi ini dalam bentuk video menarik <em>bareng</em> Master Teacher yang asik lewat <strong><a href="https://www.ruangguru.com/ruangbelajar" target="_blank" rel="noopener">ruangbelajar</a></strong>. Belajar jadi mudah dan pastinya banyak latihan soal yang <em>bikin</em> kamu antiremed!</p>
<p style="text-align: center;"><a href="https://bayar.ruangguru.com/"><img decoding="async" class="aligncenter size-medium" src="https://cdn-web-2.ruangguru.com/landing-pages/assets/ceb472c4-1feb-4a1d-afdf-4f92234a63d0.jpg" alt="CTA Ruangguru" /></a></p>
<p style="text-align: left;"><strong>Referensi:</strong></p>
<p style="text-align: left;">As’ari A.R, Tohir M, Valentino E, Imron Z, Taufiq I. (2017) Matematika SMP/MTs Kelas VIII Semester 1. Jakarta: Kementerian Pendidikan dan Kebudayaan</p>
<p style="text-align: left;"><strong>Sumber foto:</strong></p>
<p style="text-align: left;">GIF ‘Kumamon Loncat’ [Daring]. Tautan: https://giphy.com/gifs/kumamon-LVWzUCdGioDBe (Diakses: 23 Desember 2020)</p>
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<a target="_blank" rel="nofollow" href="https://play.google.com/store/apps/details?id=com.ruangguru.livestudents&hl=in">
<img src="https://cdn-web-2.ruangguru.com/static/googleplay.png" loading="lazy" alt="Button Google Play Footer " />
</a>
</li>
<li>
<a target="_blank" rel="nofollow" href="https://appgallery.huawei.com/#/app/C102352375">
<img src="https://cdn-web-2.ruangguru.com/static/huawei.png" loading="lazy" alt="Button AppGallery Footer " />
</a>
</li>
</ul>
</div>
</nav>
</div>
</div>
</div>
</div>
<div class="d-lg-none text-center">
<nav class="footer-menu social">
<p class="title">Ikuti Kami</p>
<a target="_blank" href="https://www.instagram.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/instagram.png" loading="lazy" alt="Logo Instagram Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.facebook.com/ruanggurucom/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/facebook.png" loading="lazy" alt="Logo Facebook Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://twitter.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/twitter.png" loading=" lazy" alt="Logo Twitter Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.youtube.com/ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/youtube.png?height=60&convert=webp" type="image/webp">
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<img src="https://cdn-web-2.ruangguru.com/static/youtube.png" loading=" lazy" alt="Logo Youtube Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.linkedin.com/company/ruangguru-com">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60&convert=webp" type="image/webp">
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<img src="https://cdn-web-2.ruangguru.com/static/linkedin.png" loading=" lazy" alt="Logo LinkedIn Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.tiktok.com/@ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/tiktok.png" loading=" lazy" alt="Logo TikTok Footer" width="32px" height="32px" />
</picture>
</a>
</nav>
</div>
<p class="footer-copyright">
© 2026 All Rights Reserved PT. Ruang Raya Indonesia
</p>
</div>
<style>
.bantuan-container {
position: relative;
}
.bantuan-element {
position: fixed;
z-index: 999;
display: flex;
align-items: flex-end;
justify-content: flex-end;
cursor: pointer;
transition: all 0.6s ease;
}
.bantuan-top {
bottom: 11rem;
right: 2rem;
}
.bantuan-bottom {
bottom: 2rem;
right: 2rem;
}
.bantuan-top-2 {
bottom: 15rem;
right: 2rem;
}
.bantuan-top-3 {
bottom: 19rem;
right: 2rem;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 2rem;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 2rem;
}
@media (min-width: 768px) {
.bantuan-element img {
width: auto;
transition: all 0.4s ease;
}
.bantuan-top img {
width: 140px;
}
.bantuan-bottom img {
width: 140px;
}
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 140px;
}
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 140px;
}
.bantuan-element.clicked {
bottom: 9rem;
right: 2.5rem;
}
.bantuan-element.clicked img {
width: auto;
height: 64px;
}
}
@media (max-width: 767px) {
.bantuan-top {
bottom: 8rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom {
bottom: 2rem;
right: 1.25rem;
align-items: center;
}
.bantuan-top-2 {
bottom: 12rem;
right: 1rem;
align-items: center;
}
.bantuan-top-3 {
bottom: 16rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 1.25rem;
align-items: center;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 1.25rem;
align-items: center;
}
.bantuan-element img {
width: auto;
}
.bantuan-top img,
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 96px;
}
.bantuan-bottom img,
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 96px;
}
}
.bantuan-element:hover {
transform: scale(1.05);
}
.bantuan-element img {
max-width: 100%;
height: auto;
}
</style>
<div id="bantuan-divs-container" style="position: relative" data-product="ruangguru" data-table="rg_floating_icon"></div>
<script>
class FloatingDivsComponent {
constructor(product = 'ruangguru', table = 'rg_floating_icon') {
this.container = document.getElementById('bantuan-divs-container');
this.floatingElements = [];
this.product = product;
this.table = table;
// Configuration
this.config = {
baseApiUrl: 'https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/rg_banner/views/',
apiKey: 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
maxElements: 2,
zIndexBase: 100,
};
// Build dynamic API URL based on table parameter
this.config.apiUrl = this.buildApiUrl();
this.init();
}
buildApiUrl() {
const baseUrl = this.config.baseApiUrl;
const tableName = this.table || 'rg_floating_icon';
const queryParams =
'offset=0&limit=99999&sort=rankPosition&where=(type,eq,floating)~and(showIn,anyof,blog)~and(hide,is,false)~and(product,eq,' +
this.product +
')&nested%5Bcta%5D%5Bfields%5D=Id,name,ctaId,imageUrl,ctaLink,targetUrl';
return `${baseUrl}${tableName}?${queryParams}`;
}
async init() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to initialize floating divs component:', error);
}
}
async fetchFloatingElements() {
try {
const options = {
method: 'GET',
headers: {
'xc-token': this.config.apiKey || 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
},
};
const urlNoco = this.config.apiUrl;
const response = await fetch(urlNoco, options);
if (!response.ok) {
throw new Error(`HTTP error! status: ${response.status}`);
}
const data = await response.json();
this.floatingElements = this.processApiResponse(data);
} catch (error) {
console.error('Error fetching floating elements:', error);
throw error;
}
}
processApiResponse(data) {
if (!data || !data.list || !Array.isArray(data.list)) {
return [];
}
console.log(data.list);
// Ensure we only get maximum 2 elements
const limitedElements = data.list.slice(0, this.config.maxElements);
return limitedElements;
}
renderFloatingElements() {
if (!this.container || this.floatingElements.length === 0) {
return;
}
// Additional safeguard: ensure we never render more than maxElements
const elementsToRender = this.floatingElements.slice(0, this.config.maxElements);
// Clean up existing elements and their event listeners
this.cleanupExistingElements();
// Clear existing content
this.container.innerHTML = '';
elementsToRender.forEach((element, index) => {
const floatingDiv = this.createFloatingDiv(element, index);
this.container.appendChild(floatingDiv);
});
}
cleanupExistingElements() {
// Clear existing elements (no need for event listener cleanup with CSS approach)
const existingElements = this.container.querySelectorAll('[data-floating-element]');
existingElements.forEach(element => {
element.remove();
});
}
createFloatingDiv(element, index) {
const div = document.createElement('div');
const cta = element.cta[0]; // Use the first CTA
// Add data attribute for cleanup tracking
div.setAttribute('data-floating-element', 'true');
// Apply CSS classes based on rankPosition
const positionClass = this.getPositionClass(element.rankPosition, index);
div.className = `bantuan-element ${positionClass}`;
div.style.zIndex = this.config.zIndexBase + index;
// Create the link and image
const link = document.createElement('a');
link.href = 'https://cta.ruangguru.com/' + cta.ctaId || '#';
link.target = '_blank';
// Add tracking attributes
link.setAttribute('data-tracking-event-type', 'landing_page__core__item_click');
link.setAttribute(
'data-tracking-context',
JSON.stringify({
product_name: this.product,
cta_action: 'redirection',
cta_action_detail: link.href,
item_type: 'floating',
item_name: element.name || 'Floating element',
item_category: 'payment',
item_position: index,
item_serial: null,
section_type: 'floating_item',
section_position: 'body',
section_name: 'floating_item',
})
);
const img = document.createElement('img');
img.src = element.imageUrl + '?h=200&convert=webp';
img.alt = element.name || 'Floating element';
img.loading = 'lazy';
// Add click tracking
link.addEventListener('click', () => {
this.trackClick(element, cta);
});
link.appendChild(img);
div.appendChild(link);
return div;
}
getPositionClass(rankPosition, index) {
// Define positioning classes based on rankPosition
if (rankPosition === 1) {
return 'bantuan-top'; // Top position
} else if (rankPosition === 2) {
return 'bantuan-bottom'; // Bottom position
} else {
// For additional elements, distribute them evenly
return `bantuan-${index % 2 === 0 ? 'top' : 'bottom'}-${Math.floor(index / 2) + 1}`;
}
}
trackClick(element, cta) {
// Implement click tracking logic here
console.log('Floating element clicked:', {
elementId: element.Id,
elementName: cta.name,
ctaId: cta.ctaId,
targetUrl: cta.targetUrl,
});
}
// Public method to manually refresh
async refresh() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to refresh floating elements:', error);
throw error;
}
}
// Public method to get current floating elements
getFloatingElements() {
return [...this.floatingElements];
}
}
// Initialize the component when DOM is ready
document.addEventListener('DOMContentLoaded', () => {
// Get product and table parameters from data attributes
const container = document.getElementById('bantuan-divs-container');
const product = container.getAttribute('data-product') || 'ruangguru';
const table = container.getAttribute('data-table') || 'rg_floating_icon';
new FloatingDivsComponent(product, table);
});
// Export for use in other modules if needed
if (typeof module !== 'undefined' && module.exports) {
module.exports = FloatingDivsComponent;
}
</script> <div id="wp-install-nudge" style="
position: fixed;
bottom: 0rem;
right: 0;
z-index: 999;
cursor: pointer;
"></div>
<script>
(function (w, d, s, o, f, js, fjs) {
w['Sales-Nudge-Widget'] = o; w[o] = w[o] || function () { (w[o].q = w[o].q || []).push(arguments) };
js = d.createElement(s), fjs = d.getElementsByTagName(s)[0];
js.id = o; js.src = f; js.async = 1; fjs.parentNode.insertBefore(js, fjs);
}(window, document, 'script', 'wpInstallNudge', 'https://cdn-web-2.ruangguru.com/sales-nudge/6198a95130/dist/widget.js'));
wpInstallNudge('init', { targetElementId: 'wp-install-nudge', clientTarget: 'ruangguru_blog' });
</script>
<script>
// note: disabled due to auto reload page
// var lastScrollTop = 0;
// $(window).scroll(function(event){
// var st = $(this).scrollTop();
// if (st > lastScrollTop){
// $('#wp-install-nudge').slideDown( "slow", function() {});
// } else {
// $('#wp-install-nudge').slideUp( "slow", function() {});
// }
// lastScrollTop = st;
// });
// $(document).ready(function () {
// $("#wp-install-nudge").hide();
// });
$('#wp-install-nudge').click(function(){
Analytics.track("promotion__install_nudge__click",
{
user_email: "ruangguru@blog.com",
cta_link: widgetData.dataConfig.target_link
}).catch((err) => {
console.log("tracker error", err);
});
});
</script>
</footer>
<div id="__next"></div>
<script type="speculationrules">
{"prefetch":[{"source":"document","where":{"and":[{"href_matches":"\/blog\/*"},{"not":{"href_matches":["\/blog\/wp-*.php","\/blog\/wp-admin\/*","\/blog\/wp-content\/uploads\/*","\/blog\/wp-content\/*","\/blog\/wp-content\/plugins\/*","\/blog\/wp-content\/themes\/ruangguru\/*","\/blog\/*\\?(.+)"]}},{"not":{"selector_matches":"a[rel~=\"nofollow\"]"}},{"not":{"selector_matches":".no-prefetch, .no-prefetch a"}}]},"eagerness":"conservative"}]}
</script>
<script>
async function getCtaDetails(ctaIds) {
const endpoint =
" https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/CTA/views/CTA?offset=0&limit=10&where=(ctaId,in," + ctaIds.toString() + ")";
try {
const response = await fetch(endpoint, {
headers: {
"xc-token": "-hG2nBDJzSj0agSgNtcJx97M4F02y54nUMoY6plJ",
},
});
const data = await response.json();
const ctaList = data?.list || [];
const ctaMap = new Map();
for (const ctaData of ctaList) {
ctaMap.set(ctaData.ctaId, ctaData);
}
return ctaMap;
} catch (error) {
console.error("Error fetching CTA details:", error);
return new Map();
}
}
async function replaceCTA() {
const regex = /{{cta\((‘(.*?)’|“(.*?)”)\)}}/g;
const bodyHTML = document.body.innerHTML;
const matches = Array.from(bodyHTML.matchAll(regex));
const ctaIds = matches.map((match) => {
let ctaId = match[2] ?? match[3];
return ctaId;
});
const ctaMap = await getCtaDetails(ctaIds);
const replacedHTML = bodyHTML.replace(regex, (match, _inner, ctaId1, ctaId2) => {
const ctaId = ctaId1 ?? ctaId2;
const ctaData = ctaMap.get(ctaId);
if (ctaData) {
return `<a href="https://cta.ruangguru.com/${ctaData.ctaId}" target="_${ctaData.targetType}" style="position:relative;display:inline-block;">
<img src="${ctaData.imageUrl}" loading="lazy" alt="${ctaData.altText}" />
</a>`;
} else {
return match;
}
});
document.body.innerHTML = replacedHTML;
}
</script>
<meta name="author" content="Ruangguru Tech Team">
<!-- Google Tag Manager (noscript) -->
<noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-PVNLZFT" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript>
<!-- Tracker -->
<script type="text/javascript" src="https://cdn-web-2.ruangguru.com/landing-page-web/public/staticpages/global-assets/js/cta.js"></script>
<script src="https://unpkg.com/@dotlottie/player-component@latest/dist/dotlottie-player.mjs" type="module"></script>
</body>
</html>