Matematika Ekonomi (Pertemuan 3/ Sistem Persamaan Linier)

Summary

This script discusses linear equation systems, focusing on two-variable systems and their solutions using substitution and elimination methods. It illustrates these methods with examples involving counting vehicles and calculating parking fees. The video also presents a real-world problem-solving scenario where a parking attendant charges different rates for cars and motorcycles, leading to a system of equations that are solved to find the rates and total earnings.

Takeaways

• 🧮 The script discusses linear equation systems, specifically focusing on two-variable systems where two equations are used to solve for two unknowns.
• 🛣️ An example problem is presented involving counting vehicles at an intersection, using a system of linear equations to determine the number of bicycles and motorcycles.
• 🔍 Two methods for solving linear equations are introduced: the substitution method and the elimination method.
• 🔢 In the substitution method, one equation is manipulated to express one variable in terms of the other, which is then substituted into the second equation.
• ➖ The elimination method involves manipulating both equations to cancel out one variable, allowing for the solution of the other.
• 📚 A detailed example is given for each method, showing step-by-step how to solve for the variables using the equations provided.
• 💡 A mixed method combining substitution and elimination is also explained, which can be more efficient depending on the problem.
• 💼 The script applies these mathematical concepts to a real-world scenario involving parking fees for cars and motorcycles, creating equations based on given totals and unknown individual fees.
• 🚗🏍️ The solution to the parking fee problem is found using a mixed method, first solving for one variable and then substituting it back into the equations to find the other.
• 💵 Finally, the script demonstrates how to calculate the total parking revenue for a given number of cars and motorcycles using the solved fees from the equations.

Q & A

What is the main topic discussed in the script?

The main topic discussed in the script is linear equation systems, specifically focusing on solving systems of linear equations with two variables.

What are the two methods introduced for solving systems of linear equations?

The two methods introduced for solving systems of linear equations are the substitution method and the elimination method.

How does the substitution method work in solving a system of linear equations?

The substitution method involves choosing one of the equations to solve for one variable, and then substituting that expression into the other equation to solve for the second variable.

Can you explain the elimination method as described in the script?

The elimination method involves manipulating the equations so that the same variable coefficients are aligned, and then subtracting one equation from the other to eliminate one of the variables, making it easier to solve for the remaining variable.

What is a mixed method for solving systems of linear equations?

A mixed method combines both substitution and elimination techniques. It may involve using elimination to solve for one variable and then substitution to solve for the other, or vice versa.

How does the script apply the concept of systems of linear equations to a real-world problem?

The script applies the concept to a parking fee problem where the total earnings from parking cars and motorcycles are given, and the task is to determine the individual parking fees for a car and a motorcycle.

What are the two variables represented in the parking fee problem?

In the parking fee problem, the two variables are the parking fee for one car (x) and the parking fee for one motorcycle (y).

What is the strategy for solving the parking fee problem using the mixed method?

The strategy involves first using the elimination method to find the value of one variable, and then substituting that value into one of the original equations to find the value of the other variable.

What are the final values of x and y obtained in the parking fee problem?

The final values obtained are x = 4000 (parking fee for one car) and y = 1000 (parking fee for one motorcycle).

How is the total parking revenue calculated if there are 20 cars and 30 motorcycles?

The total parking revenue is calculated by multiplying the number of cars (20) by the parking fee per car (4000) and the number of motorcycles (30) by the parking fee per motorcycle (1000), then adding the two amounts together to get 110,000.