Membuat Model Matematika Sistem Persamaan Linear Dua Variabel

Linda Ika Yuliana

22 Nov 202015:10

Summary

TLDRThis video introduces a lesson on solving real-life problems using linear equations with two variables (SPLDV). The presenter explains step-by-step how to create mathematical models from word problems, involving examples such as clothing prices, number problems, age differences, parking scenarios, and perimeter calculations. Key steps include understanding the problem, defining variables, forming equations, and solving them using appropriate methods. The video aims to simplify these concepts, helping viewers better understand SPLDV and apply it to everyday situations. It ends with a practical demonstration of finding the area of a rectangle using given dimensions.

Takeaways

📘 Linear equations with two variables (SPLDV) are used to model and solve everyday problems involving mathematical relationships.
📝 The first step in solving an SPLDV word problem is to read and understand the problem, identifying the known and unknown variables.
🔄 Convert the words of the problem into a mathematical model by assigning variables to the unknown quantities.
🔢 Solve the resulting system of linear equations (SPLDV) using methods such as substitution or elimination.
👕 Example 1: The price of 2 shirts and 1 t-shirt is 273,000 IDR, and 1 shirt and 3 t-shirts cost 320,000 IDR. This can be written as two linear equations.
➗ Example 2: The sum of two numbers is 38, and twice the first number minus the second number equals 3. This is another system of linear equations.
👫 Example 3: Rudy is 3 years younger than Prisca, and their combined age is 21. This can be modeled using SPLDV.
🚗 Example 4: In a parking lot with 24 vehicles, including cars and motorcycles, the total number of wheels is 66. This can also be solved using SPLDV.
📏 Example 5: The perimeter of a rectangle is 76 cm, and the length is 12 cm longer than the width. Use SPLDV to find the dimensions and calculate the area.
✅ Using SPLDV helps break down complex word problems into solvable mathematical models, applying real-life scenarios into systems of equations.

Q & A

What is the main topic discussed in the script?
-The main topic discussed in the script is learning about systems of linear equations with two variables (SPLDV) and how to model mathematical problems from everyday life using SPLDV.
What is the first step in solving a problem involving SPLDV?
-The first step in solving a problem involving SPLDV is to read and understand the problem statement, identifying what is given and what is asked.
How are statements in a story problem translated into mathematical terms?
-Statements in a story problem are translated into mathematical terms by assigning variables to unknown quantities and forming equations that represent the relationships described in the problem.
What is an example of a real-life problem that can be modeled using SPLDV?
-An example of a real-life problem that can be modeled using SPLDV is calculating the cost of clothes where the price of 2 shirts and 1 jacket is 273,000, and the price of 1 shirt and 3 jackets is 320,000.
What variables are used to represent the cost of a shirt and a jacket in the given example?
-In the given example, the cost of a shirt is represented by the variable 'x' and the cost of a jacket is represented by the variable 'y'.
How are the equations formed for the example involving the cost of clothes?
-The equations are formed by translating the given information into mathematical expressions: 2x + y = 273,000 for the cost of 2 shirts and 1 jacket, and x + 3y = 320,000 for the cost of 1 shirt and 3 jackets.
What is the fourth step after forming the mathematical model in SPLDV problems?
-The fourth step after forming the mathematical model in SPLDV problems is to use the solution obtained from solving the equations to answer the question posed in the story problem.
Can you provide another example of a problem that involves SPLDV?
-Yes, another example is determining the ages of Rudi and Kristen if Rudi is three years younger than Kristen and their combined age is 21 years.
How are the ages of Rudi and Kristen represented mathematically in the example?
-In the example, Rudi's age is represented by 'x' and Kristen's age by 'y'. The mathematical model is formed with the equations x = y - 3 (Rudi is three years younger) and x + y = 21 (their combined age).
What is the method used to solve the system of equations in the script?
-The script suggests using a combination of substitution and elimination methods to solve the system of equations.
Can you explain the process of elimination in the context of solving SPLDV?
-In the context of solving SPLDV, elimination involves adding or subtracting multiples of one equation from another to eliminate one of the variables, allowing the solution of the system.

Outlines

00:00

📘 Introduction to Linear Equations with Two Variables

This section introduces the topic of solving everyday problems using Systems of Linear Equations in Two Variables (SPLDV). The speaker explains that real-life problems often involve SPLDV and outlines steps for solving these problems: understanding the given information, converting word problems into mathematical models by assigning variables, solving the equations, and using the solutions to answer the original problem. A simple example involving the price of shirts and t-shirts is discussed, demonstrating how to form a system of equations.

05:03

📝 Example: Solving Word Problems Using SPLDV

In this part, more examples of creating mathematical models from word problems are given. The speaker presents a problem involving two numbers where their sum is 38, and the difference of twice the first number minus the second is 3. The process of converting these sentences into linear equations and solving them is detailed. The speaker emphasizes the importance of accurately translating verbal descriptions into mathematical statements.

10:07

👶 Example: Age-related Word Problem

Here, the speaker tackles another example, this time about ages. Rudi is 3 years younger than Priska, and together they are 21 years old. The speaker shows how to define the variables for Rudi and Priska's ages and then forms a system of equations. By solving the equations, the age of each individual can be found, demonstrating the power of SPLDV in solving such relational problems.

🚗 Example: Vehicles in a Parking Lot

This paragraph introduces a word problem about vehicles in a parking lot, where the total number of vehicles is 24, and the total number of wheels is 66. The speaker explains how to assign variables to represent the number of cars and motorcycles and create a system of equations based on the given information. The solution involves solving the system to find the number of cars and motorcycles in the lot.

📏 Example: Solving a Rectangle Problem

The final example is about finding the dimensions of a rectangle given its perimeter and the relationship between its length and width. The speaker explains how to assign variables to the length and width, form a system of equations using the perimeter formula, and solve for the dimensions. After finding the dimensions, the speaker calculates the area of the rectangle. The method of solving the system involves both elimination and substitution techniques, making this a comprehensive example of applying SPLDV.

Mindmap

Keywords

💡Sistem Persamaan Linear Dua Variabel (SPLDV)

SPLDV, or 'Linear Equation System with Two Variables,' refers to a set of two equations that involve two variables. The goal is to find the values of these variables that satisfy both equations simultaneously. In the video, SPLDV is the main topic, and the speaker teaches students how to create mathematical models from real-life problems, such as solving word problems with systems of equations.

💡Model Matematika

A 'mathematical model' is a representation of a problem using mathematical expressions and equations. The video demonstrates how to transform word problems into mathematical models by assigning variables to unknowns and forming equations based on the relationships described in the problem. Examples include converting statements about the prices of shirts and t-shirts into algebraic expressions.

💡Soal Cerita

'Soal cerita' means 'word problems' in English, referring to mathematical problems expressed through real-life scenarios or narratives. In the video, the speaker emphasizes reading and understanding word problems before converting them into mathematical models. Scenarios such as comparing ages or counting vehicles in a parking lot are examples used to illustrate this concept.

💡Variabel

A 'variable' in mathematics is a symbol, typically a letter, that represents an unknown quantity. The video shows how variables are used to represent quantities like the price of a shirt (x) or the number of vehicles (y). Understanding how to assign variables to unknowns is key in forming equations in SPLDV.

💡Harga

'Harga' means 'price' in English. In the context of the video, price is a key element in many of the word problems, such as determining the cost of two shirts and one t-shirt or comparing the prices of various items. The concept of price helps introduce variables into real-world contexts.

💡Jumlah

'Jumlah' means 'sum' or 'total.' In the video, it is used in word problems that involve summing quantities, such as the total number of vehicles or the combined ages of two people. This concept is fundamental when forming equations, as sums often provide one of the key relationships in SPLDV problems.

💡Keliling

'Keliling' refers to the perimeter of a shape, particularly a rectangle in the video. The speaker uses a problem involving the perimeter of a rectangle to explain how to create equations. By knowing the perimeter and how the length is related to the width, a system of equations can be formed to solve for the dimensions.

💡Eliminasi

'Eliminasi' or 'elimination' is one method for solving systems of linear equations. It involves eliminating one of the variables by adding or subtracting the equations. In the video, the speaker explains how this method can be used to simplify the solution process by removing one variable, leaving a simpler equation to solve.

💡Substitusi

'Substitusi' or 'substitution' is another method for solving systems of equations. It involves solving one equation for one variable and then substituting that expression into the other equation. The video explains how substitution can be used to find the values of the variables in word problems.

💡Koordinasi Persegi Panjang

The concept of 'koordinasi persegi panjang,' or 'rectangular dimensions,' is used in one of the word problems discussed in the video. The problem involves finding the length and width of a rectangle given its perimeter and the relationship between the length and width. This demonstrates how geometric concepts are integrated into algebraic problem-solving.

Highlights

Introduction to the lesson on systems of linear equations in two variables (SPLDV) using real-life problems.

Explanation of how real-life problems can be solved using SPLDV.

Steps to solve SPLDV word problems: read and understand the problem, convert it to a mathematical model, solve the model, and use the solution to answer the question.

Example 1: Modeling the cost of clothes. 2 shirts and 1 T-shirt cost 273,000 IDR, while 1 shirt and 3 T-shirts cost 320,000 IDR.

Demonstration of converting the first example into a mathematical model using variables for unknowns.

Example 2: Modeling the sum and difference of two numbers. Their sum is 38, and twice the first number minus the second is 3.

Converting the second example into a mathematical model and solving it.

Example 3: Modeling age differences. Rudi is 3 years younger than Priska, and their combined ages are 21.

Explanation of converting age-related word problems into mathematical models.

Example 4: Modeling the number of vehicles and their wheels. 24 vehicles with a total of 66 wheels.

Conversion of vehicle problem into a mathematical model using the number of cars and motorcycles as variables.

Simplifying the equations in the vehicle example to form SPLDV.

Example 5: Modeling the dimensions of a rectangle given its perimeter and the relationship between length and width.

Converting the rectangle problem into a mathematical model and solving it to find the area.

Summary of the process of creating mathematical models from word problems and solving them using SPLDV.

Encouragement to practice and understand SPLDV problems for better comprehension.