Sistem persamaan linear dua variabel (SPLDV) Metode subtitusi, Eliminasi dan Campuran

Summary

This educational video script introduces methods for solving systems of linear equations with two variables. It covers the elimination method, substitution method, and a mixed approach. The script guides viewers through each method using a specific problem, demonstrating step-by-step solutions. The aim is to make the process easy to understand and encourage viewers to apply these techniques to similar problems, enhancing their mathematical problem-solving skills.

Takeaways

• 📚 The video discusses solving systems of linear equations with two variables using elimination, substitution, and a mixed method.
• 🔢 The example problem given is 2x + y = 9 and 3x + 2y = 15, which is solved step by step in the video.
• 📝 The substitution method is demonstrated first, where one equation is solved for y in terms of x, and then substituted into the other equation.
• 🧩 In the elimination method, the video shows how to eliminate one variable by making the coefficients of x or y the same in both equations and then subtracting one from the other.
• 🔄 The mixed method combines both elimination and substitution, where elimination is used first to simplify the system, and then substitution is applied to find the values of x and y.
• 📉 The video explains the importance of considering the signs of coefficients when performing elimination, as the signs determine whether to add or subtract the equations.
• 📌 The presenter emphasizes the need to simplify the equations after each step to make the process easier and to avoid mistakes.
• 📐 The video concludes with the solution to the example problem, which is x = 3 and y = 3, using both the elimination-substitution and mixed methods.
• 💡 The video encourages viewers to practice these methods with the same problem to ensure understanding and to apply the techniques to other similar problems.
• 🌐 The video is part of a mathematics education channel, aiming to provide beneficial content and potentially serve as a form of continuous good deed (amal jariyah).

Q & A

What is the main topic of the video?

The main topic of the video is solving systems of linear equations with two variables using three different methods: substitution, elimination, and a mixed method.

What is the first equation presented in the video?

The first equation presented in the video is 2x + y = 9.

What is the second equation presented in the video?

The second equation presented is 3x + 2y = 15.

How is the substitution method applied to solve the system of equations?

In the substitution method, one variable (y) is isolated from the first equation (y = 9 - 2x), then substituted into the second equation (3x + 2(9 - 2x) = 15) to solve for x. Once x is found, it is substituted back to find y.

What are the values of x and y using the substitution method?

Using the substitution method, the values of x and y are both 3.

How does the elimination method differ from the substitution method in the video?

In the elimination method, the coefficients of one variable (x or y) are made equal by multiplying the equations. The corresponding terms are then subtracted to eliminate one variable, allowing the other variable to be solved directly.

What are the steps for using the elimination method to solve the system?

First, both equations are multiplied by appropriate factors so that the x-coefficients are equal. The equations are then subtracted to eliminate x, allowing the solution for y. Finally, the value of y is substituted back into one equation to find x.

What is the result when using the elimination method to solve the system?

Using the elimination method, the values of x and y are again both 3.

What is the mixed method used in the video?

The mixed method combines both elimination and substitution. First, elimination is used to remove one variable, and then substitution is used to find the remaining variable.

What is the final conclusion regarding the system of equations using all three methods?

The final conclusion is that regardless of the method used (substitution, elimination, or mixed), the solutions for x and y are both 3.

Outlines

00:00

📘 Introduction to Solving Linear Equations

The speaker begins by greeting the audience in Indonesian and introducing the topic of the video, which is solving systems of linear equations with two variables. They plan to discuss three methods: elimination, substitution, and a combination of both. The speaker encourages the audience to like, subscribe, comment, and share the video, hoping it will be beneficial and a form of continuous charity. They then dive into the problem at hand, which involves two equations: 2x + y = 9 and 3x + 2y = 15. The speaker chooses to solve the problem using the substitution method, explaining each step in detail, including transforming one of the equations to isolate y, and then substituting this expression into the other equation to find the value of x. After finding x, they substitute it back to find the value of y, concluding that x = 3 and y = 3.

05:06

🔍 Method of Elimination Explained

In this segment, the speaker explains how to use the elimination method to solve the same system of equations. They label the equations as 'persamaan 1' and 'persamaan 2' and guide the audience through the process of eliminating one variable, in this case, x. They demonstrate how to multiply each equation by certain factors to align the coefficients of x, allowing for the elimination of x when the equations are added or subtracted. The speaker shows the calculations, leading to the isolation of y, and then solves for y. After finding the value of y, they substitute it back into one of the original equations to find the value of x, concluding with the same solution of x = 3 and y = 3.

10:08

🧩 Combining Elimination and Substitution

The speaker introduces a mixed method, combining both elimination and substitution to solve the system of equations. They start by eliminating x using the elimination method, similar to the previous paragraph, and then proceed to use substitution to find the values of x and y. The speaker carefully explains the process of multiplying the equations to align the coefficients of x and y and then subtracting one equation from the other to eliminate x. After obtaining an equation with only y, they solve for y and then substitute this value back into one of the original equations to find x. The final solution is again x = 3 and y = 3, emphasizing that the method of solving does not change the outcome.

15:09

🌐 Closing Remarks

The speaker concludes the tutorial with a closing remark in Indonesian, wishing the audience peace and blessings. They have successfully covered the methods of elimination, substitution, and a combination of both for solving systems of linear equations with two variables. The video aims to provide a clear and comprehensive understanding of these mathematical techniques.

Keywords

💡System of Linear Equations

A system of linear equations refers to a collection of two or more linear equations involving the same set of variables. In the context of the video, the system of linear equations is the main subject matter, with the script discussing methods to solve such systems. The video provides examples of systems with two variables, where each equation represents a straight line, and the solution to the system is the intersection point of these lines.

💡Substitution Method

The substitution method is a technique used to solve a system of linear equations by expressing one variable in terms of another from one equation and then substituting this expression into the other equation. The video script illustrates this method by choosing one of the equations to solve for one variable, and then using this expression to find the value of the second variable from the second equation.

💡Elimination Method

The elimination method is a process used to solve systems of linear equations by adding or subtracting equations in such a way that one variable is eliminated, allowing the solution to be found for the remaining variable. The script describes this method by showing how to manipulate the equations to eliminate one of the variables, thus simplifying the system to a single equation with one variable.

💡Mixed Method

The mixed method, as mentioned in the script, refers to a combination of the substitution and elimination methods to solve a system of linear equations. The video explains how to use both techniques in a step-by-step process, first eliminating one variable and then substituting the result back into one of the original equations to find the value of the other variable.

💡Variables

In the context of the video, variables are the unknowns in the equations that the methods aim to solve for. The script uses 'x' and 'y' as variables in the equations, and the goal of the methods discussed is to find the values of these variables that satisfy both equations in the system.

💡Coefficients

Coefficients are the numerical factors that multiply the variables in the equations. The script refers to coefficients when discussing how to manipulate the equations, such as multiplying one equation by a certain number to align the coefficients of a variable before applying the elimination method.

💡Solving for a Variable

Solving for a variable means finding an expression for one variable in terms of the other or in terms of constants. The video script demonstrates this by showing how to isolate one variable in an equation, which is a crucial step in both the substitution and mixed methods.

💡Like, Subscribe, Comment, Share

These terms are common calls to action on video platforms, encouraging viewers to engage with the content. In the script, they are used as a request for viewer interaction, indicating that the video's content is meant to be educational and beneficial, and the creators hope for it to be shared for the benefit of others.

💡Amil Jariyah

Amil jariyah is an Islamic concept referring to good deeds that continue to provide rewards even after the doer has passed away. In the script, the presenter hopes that the video will be considered an amil jariyah, suggesting that the educational content has lasting value and benefits for the viewers.

💡Persamaan

In the script, 'persamaan' is the Indonesian word for 'equation.' The video discusses solving systems of linear equations, so 'persamaan' is used repeatedly to refer to the individual equations within the system that are being manipulated and solved.

💡Positive and Negative Signs

The video script mentions the importance of considering the signs (positive or negative) when performing operations on equations, especially during the elimination method. Correctly handling these signs is crucial for obtaining the correct solution to the system of equations.

Highlights

Introduction to solving systems of linear equations with two variables using elimination, substitution, and mixed methods.

Explanation of the elimination method for solving systems of equations.

Step-by-step guide on how to use substitution to solve a system of equations.

The importance of rearranging equations to isolate variables for substitution.

Demonstration of substituting one equation into another to find the value of a variable.

Solving for 'x' using the substitution method in a system of linear equations.

Finding the value of 'y' after determining 'x' in a system of equations.

Verification of the solution by substituting the found values back into the original equations.

Introduction to the mixed method, combining elements of both elimination and substitution.

How to eliminate one variable by manipulating the coefficients of the equations.

Using the elimination method to simplify the system of equations.

Explanation of the sign changes when eliminating variables in a system of equations.

Solving for 'y' using the mixed method after eliminating 'x'.

Final solution for the system of equations using the mixed method.

Conclusion and summary of the methods discussed for solving systems of linear equations.

Encouragement for viewers to practice these methods for better understanding.

Closing remarks with a wish for the video to be beneficial and a source of continuous learning.

Transcripts

Indonesia hei hei bagi salamualaikum

warahmatullahi wabarakatuh ketemu lagi

dan channel kami matematika hebat nah

kali ini kami akan mencoba membahas

materi itu tentang sistem persamaan

linear dua variabel dengan menggunakan

metode eliminasi lalu metode subtitusi

yang terakhir metode campuran namun

sebelum kita lanjut jangan lupa like

subscribe comment dan share video kami

semoga videonya bermanfaat dan

mudah-mudahan bisa menjadi amal jariyah

untuk kami tentunya Nah sekarang

langsung saja kita bahas soalnya

Oke untuk soal kita kali ini itu

diketahui pasang pertama yaitu 2 x

ditambah y = 9 lalu persamaan yang kedua

yaitu 3 x ditambah 2 y = 15 lah yang

pertama kita akan mencoba menjawab soal

kita kali ini dengan menggunakan metode

subtitusi oke nah perhatikan langkah

demi langkahnya Nah berarti kan kita

kali ini mempunyai dua buah persamaan

Nah dari salah satu persamaan ini kita

harus membuat dia jadi X = atau Y =

terserahmu persamaan mana yang harus

kelewat namun biar lebih mudah

perhatikan para agar yang berdiri

sendiri tidak ada kofesien nya yaitu ye

Oke nah bersama satu ini itu akan kita

Rhoma bentuknya menjadi

di Y = positif 9 Nah kalau positif 2x

mineral jadi negatif 2x ini kita

misalkan sebagai persamaan 1 Raya

dibawah ini sebagai persamaan2 karenanya

kita pakai metode subtitusi maka

sekarang langkah selanjutnya itu akan

kita subtitusikan subtitusi persamaan 1

ke persamaan2 ketikan persamaan dua

yaitu 3 x ditambah 2 y = 15 dan setiap

yang ada isinya disini itu kita akan

kita ganti dengan persamaan satu ini Oke

maka sekarang jadinya itu 3x ditambah

dua Nah akhirnya kita ganti dengan 9 Dek

orang2x

Oh ya akan sampai dengan 15 lanjut 3x

ditambah dua kali 9-18 lalu dua kali

negatif 2x hasilnya negatif 4x = 15 3x

dikurang empat X kita peroleh hasilnya

negatif 1x atau negatif X aja sama

dengan 15 the positive 18 Kalau pindah

rumah jadi negatif 18 negatif x = 15

dikurang 18 kita peroleh hasilnya dd3

maka nilai x saja negatif dibagi negatif

hasilnya positif maka nilai m yang kita

peroleh tiga lanjutkanlah kita pakai

metode subtitusi maka langkah

selanjutnya akan kita subtitusikan lagi

dengan subtitusi nih

Hai x = 3 oke pertama drama yang

mudahnya oke yang mudah nyamuk pertama

satu boleh dua boleh nemunya mudahnya

kebersamaan satu saja perhatikan

persamaan 1 tadi y = 9 dikurang 2 x maka

y = 9 dikurang dua kalinya perhatikan

esnya Sara itu kita ganti dengan tiga

maka y = 9 dikurang dua kali 36 y = 9

kurang enam berapa itu ti3 maka terakhir

kita peroleh nilai x = 3 dan Y = 3 Nah

ini dia sistem persamaan linear dengan

menggunakan metode subtitusi gemukan

sangat gampang dan sangat mudah kali

tentunya lanjut dia lebih paham masih

dengan soal yang sama

kita akan pakai metode eliminasi

perhatikan langkah demi langkahnya

mahasiswa yang sama2 x ditambah y = 9

Halo 3 x ditambah 2 y = 15 kita akan

mencoba menjawab soal kita kali ini

dengan menggunakan metode eliminasi Oke

kita angkat kita misalkan yang pertama

ini sebagai persamaan 1 dan dibawahnya

sebagai persamaan 2 dan kita akan

mengidentifikasi terlebih dahulu

terserah mau yang eksotik kalian

eliminasi atau yang parabelle yang

kalian eliminasi terserah hati

jawabannya pasti sama sebagai Nadia

mudah yang X saja sepeda ulung 2x Oke

Solid kita tulis disini lebih dahulu ke

Kimi nasi Edi minus sih

variabel-variabel ngapain tuh Kalian

hilangkan lebih dahulu yaitu Paramex

saja eh persamaan 1 dan 2 fat32 x

ditambah y = 9 3 x ditambah 2 y = 15

karena yang kita eliminasi yaitu

variabel x maka Perhatikan angka di

depan para Lex Oke angka depan parabek

yang di atas ada kedua yang dibawa ada

angka 36 sana akan kita kalikan

kebalikannya yang diatasnya yang kita

kali tiga yang dibawanya kita kali dua

kalau tadi kan di atasnya dua dibawahnya

tiga nah sekarang yang di atas yang kita

kali tiga yang dibawahnya kita kali

Hai lanjut MP3 ini kita kalikan 11 ke

depan kayak 2y lele 2x y dan seminar

Rabbani tiga kali 2x hasilnya 6 eh lalu

tiga kali hasilnya 3 y = 3 kali 9

hasilnya 27 lalu dua kali 3x hasilnya 6x

ditambah dua kali 2y hasilnya 4y lalu 2D

kali 15 hasilnya 30 Perhatikan ya kita

hilangkan variabel x hebat ikan angka

yang ada pada batinnya nih tandanya

sama-sama positif Nah kalau di sini

tandanya sama-sama positif atau

sama-sama negatif maka Disini di Pura

itu perlu kalian ingat kalau tandanya

sama sama-sama positif atau sama-sama

negatif maka di sini tandanya kurang

lanjut 6 X dikurang 6th

Z3 y dikurang 4 y kita peroleh negatif

1/2 gathegi saja sama dengan 27 dipuran

30 kita peroleh hasilnya negatif 3

mackaye saja = negatif kali negatif

hasilnya pop positif nadi lagi kita

dapat yaitu positif tiga lanjut kita

akan mencari nilai x nya lagi Oke

caranya alien ini nasi kalau tadi kan

variabel x yang kita interaksi antara

eliminasi bye Iya Bel y persamaan 1 dan

2 tandingan 2 x ditambah y = 9 Lalu 3 x

ditambah 2 y = 15 yang mau kita

tekan pada diet maka perhatikan akaya di

depan para beli disini Yes aja kalau ya

saja itu sebenarnya ada angka 1 di sini

tapi tidak ditulis oke lalu yang

dibawahnya ada kak2 maka dirinya akan

kita kalikan yang di atas kita kali dua

yang di bawah kita kali satu oke

perhatikan diatas angka 1 di bawah angka

2 maka kebalikannya kita kalikan di babi

atasnya kita tali2 dibawahnya kita kali

satu oke lanjut dua dikali dua X kita

peroleh 4x Lalu 2 dikali 1 y kita

peroleh 2y = 2 dikali 9 kita peroleh 18

lanjut satu kali 3x kita peroleh 3x

kalau satu dikali 2 yg kita peroleh 2y

akan sama dengan satu kali 15 kita

peroleh 15

Hai perhatikan yang mau kita hilangkan

variabel yg kebetulan di depan para

begini tanahnya sama-sama positif ingat

kali lagi tapi sudah kita bahas kalau di

depan parable yang akan kita hilangkan

tandanya sama maka di sini tandanya

kurang lanjut 4 X dikurang 3 x kita

peroleh hanya X atau 1x = kalau dua i2i

habis 18 dikurang 15 kita peroleh 3 maka

hasil akhir eh kita peroleh 3 dan Y = 3

oke Kini dia jawaban kalau kita pakai

metode eliminasi Oke terakhir biar

kalian benar-benar paham Sekarang kita

akan masuk ke metode campuran yaitu

campuran antara eliminasi dan substitusi

pasti dengan soal yang sama

Hai racikan langkah demi langkahnya

diketahui soalnya yaitu 2 x ditambah y =

9 Lalu 3 x ditambah 2 y = 15 kita akan

mencoba menjawab soal kita kali ini

dengan menggunakan metode campuran Oke

kita misalkan yang di atasnya sebagai

persamaan 1 dan yang dibawah ini sebagai

persamaan2 pertama kita pakai metode

eliminasi terlebih dahulu nah kalian

kalau mau yang subtitusi dulu juga boleh

ya eliminasi yang dulu juga boleh Indah

dia campurkan kita selang-seling yang

pertama eliminasi yang kedua barulah

tisu subtitusi atau musuh kursi terlebih

dahulu juga boleh yang nanti baru yang

eliminasi Oke tadi kan kalau kali ini

kita pakai yang eliminasi terlebih

dahulu

Hai Ellie ini nasi Oke kita akan

mengeliminasi parable X terlebih dahulu

persamaan 1 dan 2 kg segini sama satunya

2 x ditambah y = 9 Lalu 3 x ditambah 2 y

= 15 iamo kita hilangkan variabel x maka

Perhatikan angka di depan para bank x

oke diatas agar kedua di bawah ada

Ketiga makan di sini kita kalikan yang

diatasnya yang kita tali tiga yang

bawahnya kita kali tua lanjut tiga

dikali 2x kita peroleh hasilnya keenam

eh lalu ditambah tiga kali ye kita

peroleh 3 y = 3 kali 9 hasilnya 27

lanjut dua kali 3x

ia peroleh 6x lalu ditambah dua kali 2y

hasilnya 4y = dua kali 15 kita peroleh

30 yang mau kita hilangkan parable tak

bakal Perhatikan angka di depan para

belek ini dia sama-sama positif kalau

tandanya sama-sama positif maka di sini

tandanya pura ini perlu kalian ingat 6 X

dikurang 6 eh habis lalu 3i dikurang 4 y

kita peroleh negatif 1 itu atau negatif

y = 27 dikurang 30 kita peroleh negatif

3 mackaye saja negatif bagi negatif

positif Maka hasilnya itu adalah positif

tiga ini baru nilai y karena yang kita

pakai metode campuran tadi sudah kita

pakai eliminasi maka sekarang kita pakai

subtitusi subtitusi

Hai nilai y = 3 ke persamaan propane

nantikan kalian boleh pilih mau kalian

substitusikan nilai gizi = 3 ke

persamaan 1 boleh atau ke persamaan2

juga boleh jawabannya pasti sama oke

yang mudanya ke pertama satu saja Oke

perhatikan persamaan 12 x ditambah y = 9

sekarang setiap yay ada di sini itu akan

kita ganti dengan tiga maka sekarang

jadinya itu 2x ditambah gantinya menjadi

3 = 9 mereka 2x = 9 di kurang 3x saja =

9 perang tiga hasilnya 6 lalu dibagi dua

enam bagi2 kita Purwati 3 maka hasil

akhirnya X kita dapat hasilnya tiga dan

Y kita dapat juga di tiga oke Ini dia

jawaban untuk keseluruhan metode yang

kita akan baik eliminasi-substitusi

maupun campuran jawabannya tetap sama x

= 3 dan G = 3 Ok demikian tutorial

singkat kami tentang sistem persamaan

linear dua variabel menggunakan metode

eliminasi subtitusi dan campurkan semoga

videonya bermanfaat lebih murah kami

mohon maaf kami tutup dengan

Assalamualaikum warahmatullahi

wabarakatuh ya