Aplikasi SPLDV dalam kehidupan sehari-hari

Summary

In this video, the concept of solving two-variable linear equations (SPLDV) is explained through real-life examples. The first problem involves determining the price of a notebook and pencil using a system of equations based on given purchase scenarios. The second problem applies the same method to calculate the total income from parking fees for cars and motorbikes, considering the number of vehicles and wheels. The speaker demonstrates step-by-step how to set up equations and solve them using the elimination method, providing clear and practical examples of how SPLDV can be used in everyday situations.

Takeaways

• 😀 The video introduces the application of two-variable linear equations in everyday life using a real-world problem about purchasing notebooks and pencils.
• 😀 The first step in solving a system of linear equations is to define variables for unknowns, like x for the price of a notebook and y for the price of a pencil.
• 😀 The given problem presents two equations based on the total cost of items purchased: 4 notebooks and 3 pencils, and 2 notebooks and 4 pencils.
• 😀 To solve the system of equations, the elimination method is used to eliminate one variable (in this case, x) by making the coefficients of x equal in both equations.
• 😀 The process involves multiplying the equations to match the coefficients, subtracting them, and solving for the remaining variable (y).
• 😀 After finding y = 2,500, the value of the pencil, substitution is used in one of the original equations to solve for x, the price of a notebook.
• 😀 The final solution gives the price of a notebook as Rp 3,000 and the price of a pencil as Rp 2,500.
• 😀 Another real-life problem is introduced involving a parking lot with cars and motorbikes. The goal is to determine the income from parking fees based on the number of vehicles.
• 😀 Similar to the first problem, the total number of vehicles and the total number of wheels are used to create a system of equations for cars (4 wheels) and motorbikes (2 wheels).
• 😀 Using the elimination method again, the system is solved, and the number of cars (34) and motorbikes (56) are determined.
• 😀 The income from the parking lot is calculated by multiplying the number of cars by the parking fee for cars (Rp 5,000) and the number of motorbikes by the parking fee for motorbikes (Rp 2,000), resulting in a total income of Rp 282,000.

Q & A

What is the first problem discussed in the video?

The first problem is about determining the price of a notebook and a pencil, given two purchase scenarios and their corresponding total prices.

How are the variables for the notebook and pencil denoted in the solution?

In the solution, the price of the notebook is denoted as 'x' and the price of the pencil is denoted as 'y'.

How is the system of equations formed in the first problem?

The system of equations is formed based on the given prices for two scenarios: buying 4 notebooks and 3 pencils for Rp 19,500, and buying 2 notebooks and 4 pencils for Rp 16,000.

What method is used to solve the system of equations?

The elimination method is used to solve the system of equations. The x variable is eliminated first by multiplying and adjusting the coefficients.

How are the coefficients of the equations adjusted in the elimination process?

The coefficients are adjusted by multiplying the first equation by 1 and the second equation by 2 to make the x-coefficients equal (both 4).

What is the final price of a pencil and a notebook?

The price of a pencil is Rp 2,500 and the price of a notebook is Rp 3,000.

What is the second problem discussed in the video?

The second problem involves determining the income from parking fees, where there are 90 vehicles in a parking lot consisting of cars and motorbikes, with a total of 248 wheels.

How are the variables for cars and motorbikes denoted in the second problem?

In the second problem, the number of cars is denoted as 'a' and the number of motorbikes is denoted as 'b'.

What system of equations is used to solve the parking fee problem?

The system of equations is: 'a + b = 90' (the total number of vehicles) and '4a + 2b = 248' (the total number of wheels).

How is the income from parking fees calculated?

The income is calculated by multiplying the number of cars (34) by Rp 5,000 and the number of motorbikes (56) by Rp 2,000, then summing the results.

What is the total income from parking fees in the second problem?

The total income from parking fees is Rp 282,000 (Rp 170,000 from cars and Rp 112,000 from motorbikes).

Why is the substitution method used in the first problem to find the price of the notebook?

The substitution method is used to find the price of the notebook by substituting the value of 'y' (the price of the pencil) into the first equation, allowing the solution for 'x' (the price of the notebook).