Sistem persamaan linear tiga variabel dengan metode substitusi

Summary

In this video tutorial, the presenter demonstrates how to solve a system of three linear equations with three variables using the substitution method. The step-by-step explanation covers how to isolate one variable, substitute it into the other equations, and simplify the system to solve for the remaining variables. By carefully solving each equation and substituting values, the presenter finds the values of x, y, and z. The tutorial provides an easy-to-understand walkthrough, making it an excellent resource for students learning this method of solving linear equations.

Takeaways

• 😀 Introduction to the topic: The video covers solving a system of linear equations with three variables using substitution.
• 😀 Step 1: Start by selecting any of the three given equations and solve for one variable, e.g., X = expression.
• 😀 Step 2: Substitute the expression of the selected variable (like X) into the other two equations.
• 😀 Step 3: Simplify the resulting equations to reduce the number of variables. This may lead to new equations.
• 😀 Step 4: Continue the substitution process by choosing one of the simplified equations to solve for another variable.
• 😀 Step 5: Substitute the value of the newly found variable into the other equations until all variables are solved.
• 😀 Example: Starting with the equation X = 5 - 2Y - 2Z, substitute it into the second and third equations.
• 😀 Tip: When simplifying, you can divide the equation by a common factor to make the numbers easier to work with.
• 😀 After solving for one variable, substitute the results into the remaining equations to find the values of the other variables.
• 😀 The final solution provides the values of X, Y, and Z, which in this case are 1, 4, and -2 respectively.

Q & A

What is the main topic of the video?

The main topic of the video is solving a system of linear equations with three variables (x, y, z) using the substitution method.

What are the three linear equations provided in the tutorial?

The three linear equations provided are: 1. x + 2y + 2z = 5 2. 2x + y + z = 4 3. 3x - y + 2z = -5

Which equation is chosen for substitution, and why?

The first equation is chosen for substitution because it can be easily rearranged to solve for x in terms of y and z.

How is the first equation rearranged?

The first equation, x + 2y + 2z = 5, is rearranged to x = 5 - 2y - 2z.

What is the next step after rearranging the first equation?

After rearranging the first equation, the expression for x (x = 5 - 2y - 2z) is substituted into the second and third equations.

What happens when the substitution is made in the second equation?

Substituting the expression for x into the second equation simplifies it, leading to the equation -3y - 3z = -6, which is then simplified further to y + z = 2.

How is the third equation affected by the substitution?

Substituting the expression for x into the third equation simplifies it to -7y - 4z = -20, which is then further simplified to 7z = 3z, giving a result of z = -2.

How is the value of y determined?

The value of y is determined by substituting z = -2 into the equation y = 2 - z. This results in y = 4.

How is the value of x calculated?

The value of x is calculated by substituting y = 4 and z = -2 into the rearranged first equation (x = 5 - 2y - 2z). This results in x = 1.

What is the final solution to the system of equations?

The final solution to the system of equations is x = 1, y = 4, and z = -2.