Cara menentukan himpunan penyelesaian sistem persamaan linear tiga variabel

Summary

This educational video tutorial explains how to solve a system of linear equations with three variables using the elimination method. The instructor breaks down the process step by step, demonstrating how to eliminate variables and simplify equations. By solving for x, y, and z, viewers learn how to manipulate equations for easy elimination, culminating in finding the values of the variables: x = 1, y = 2, and z = 3. The video emphasizes clarity and simplicity, making complex mathematical concepts accessible and easy to understand for learners.

Takeaways

• 😀 Introduction to solving a system of three linear equations with three variables using the elimination method.
• 😀 Encourages viewers to like, subscribe, comment, and share the video to support the channel.
• 😀 The three given equations for the problem are: 2x + 3y - z = 5, x + 2y + z = 8, and 3x - y + 2z = 7.
• 😀 The goal is to determine the values of x, y, and z in the system of equations.
• 😀 Step 1: Eliminate variable z using equations 1 and 2 by aligning the coefficients of z and performing operations.
• 😀 After elimination of z, the new equation (Equation 4) is obtained: 3x + 5y = 13.
• 😀 Step 2: Eliminate z again using equations 1 and 3 to get the new equation (Equation 5): 7x + 5y = 17.
• 😀 Step 3: Eliminate variable y by subtracting equation 5 from equation 4 and solve for x, which results in x = 1.
• 😀 Step 4: Substitute x = 1 into equation 4 to solve for y, yielding y = 2.
• 😀 Step 5: Substitute x = 1 and y = 2 into equation 2 to solve for z, yielding z = 3.
• 😀 Final solution: The values of the variables are x = 1, y = 2, and z = 3, solving the system of equations.

Q & A

What is the goal of the video tutorial?

The goal of the video tutorial is to explain how to solve a system of linear equations with three variables using the elimination method.

What are the three equations given in the problem?

The three equations are: 1) 2x + 3y - z = 5, 2) x + 2y + z = 8, and 3) 3x - y + 2z = 7.

How does the elimination method work?

The elimination method works by manipulating the equations to eliminate one variable at a time, simplifying the system until it can be solved for the remaining variables.

Why does the video first focus on eliminating variable z?

The video begins by eliminating variable z because it is the most straightforward variable to eliminate based on the coefficients in the equations.

What is the result after eliminating variable z from equations 1 and 2?

After eliminating variable z, the result is the new equation 3x + 5y = 13, referred to as Equation 4.

What steps are taken to eliminate z between equations 1 and 3?

To eliminate z, Equation 1 is multiplied by 2 and Equation 3 is left unchanged. Then, the two equations are subtracted to eliminate the z terms.

What is the new equation obtained after eliminating z from equations 1 and 3?

The new equation obtained is 7x + 5y = 17, referred to as Equation 5.

How does the video eliminate the variable y from equations 4 and 5?

The variable y is eliminated by subtracting Equation 4 from Equation 5, as both equations have the same coefficient for y. This results in the equation 4x = 4.

What value of x is found in the elimination process?

The value of x is found to be 1 after solving the equation 4x = 4.

How are the values of y and z determined after finding x?

After finding x = 1, the value of y is determined by substituting x into Equation 4, resulting in y = 2. Finally, the value of z is found by substituting x = 1 and y = 2 into Equation 2, yielding z = 3.