SPLTV Kelas 10 Kurikulum Merdeka

Summary

In this educational video on algebra and linear equations, the instructor introduces the concept of solving systems of three-variable linear equations (SPLTV). The lesson covers the general form of SPLTV equations, different methods to solve them, including substitution and elimination, and demonstrates how to apply these techniques to find solutions for variables. Additionally, the instructor presents real-life problems, like determining the prices of items from a shopping scenario, showing how to model such problems into systems of linear equations. By the end, students will be able to understand, solve, and model everyday situations as SPLTV problems.

Takeaways

• 😀 SPLTV stands for System of Linear Equations with Three Variables, an extension of SPLDV (two variables).
• 😀 The learning objectives include understanding the general form of SPLTV, solving it, and applying it to real-world problems.
• 😀 The general form of an SPLTV consists of three equations with three variables: x, y, and z.
• 😀 A system of equations is called 'linear' when the variables have an exponent of 1.
• 😀 The key to solving SPLTV is eliminating one variable at a time, often using the substitution and elimination methods.
• 😀 The method shown is a combination of substitution and elimination, often referred to as the 'combination method'.
• 😀 The first step in solving SPLTV involves eliminating one variable (e.g., x) from two equations.
• 😀 Once two equations with two variables are obtained, further elimination allows for solving the remaining variables.
• 😀 Substituting the values of variables back into the original equations allows for determining the solution for the system.
• 😀 A real-world example is provided, where the prices of items (pencil, book, and eraser) are calculated based on purchases by three people (Ayu, Bimo, and Candra).
• 😀 The lesson ends with an invitation for students to practice solving similar problems as homework.

Q & A

What is the main objective of learning SPLTV (System of Linear Equations with Three Variables)?

The main objectives are to understand the general form of SPLTV, solve SPLTV equations, and model real-life problems into SPLTV format.

How is SPLTV different from the previously learned SPLDV?

SPLDV involves two variables, while SPLTV involves three variables (x, y, and z).

What is the general form of an SPLTV equation?

The general form of an SPLTV equation is: a1x + b1y + c1z = D1, a2x + b2y + c2z = D2, a3x + b3y + c3z = D3.

What methods can be used to solve a system of linear equations with three variables?

The methods include substitution, elimination, and a combined approach, with the combined method (using both substitution and elimination) being the most commonly used.

How do you solve for variables x, y, and z in a system of linear equations?

You start by eliminating one variable at a time from the equations, then solve for the remaining variables step by step using substitution.

What is the significance of the elimination method in solving SPLTV?

The elimination method allows you to remove one variable at a time from the system, simplifying the equations and making it easier to solve for the remaining variables.

How does the combined method work in solving SPLTV?

The combined method involves using both substitution and elimination techniques to eliminate variables and simplify the system of equations, leading to a solution.

What are the steps involved in solving a sample SPLTV problem?

First, eliminate variables from pairs of equations, then solve for the remaining variables using substitution. Finally, substitute values back to find the complete solution for all variables.

What is the approach for solving word problems that require setting up SPLTV?

Start by defining the variables (e.g., prices of items), then write the system of equations based on the problem's given conditions, and solve using methods like elimination and substitution.

Can you give an example of how to model a word problem into SPLTV?

For example, in the problem where Ayu, Bimo, and Candra are buying items, you define x as the price of a pencil, y as the price of a book, and z as the price of an eraser. Then, form equations based on the quantities each person bought and the total cost they paid.