Sistem Persamaan Linier Dua Variabel (SPLDV) Metode SUBTITUSI

Summary

In this educational video, the presenter walks viewers through solving linear equations with two variables using the substitution method. Three examples are worked through step-by-step: solving the equations 2x + 3y = 8 and 3x + y = 5; x + 2y = 1 and 3x - y = 10; and 2x + y = 8 and x - y = 10. The tutorial focuses on simplifying equations, substituting values, and solving for x and y, making the concepts clear and accessible for learners. The presenter encourages viewers to comment with any alternative methods or questions.

Takeaways

• 😀 The video focuses on solving linear equations with two variables using the substitution method.
• 😀 The first example shows how to solve the system: 2x + 3y = 8 and 3x + y = 5 by substituting one equation into the other.
• 😀 The substitution method involves isolating one variable and substituting it into the other equation to solve for the second variable.
• 😀 In the first example, after substituting y = 5 - 3x into the first equation, the solution for x is found to be 1 and y equals 2.
• 😀 The second example involves solving the system x + 2y = 1 and 3x - y = 10 using substitution.
• 😀 After isolating x in the first equation, x = 1 - 2y is substituted into the second equation to find the values of x and y.
• 😀 In the second example, the solution to the system is found to be x = 3 and y = -1 after solving for both variables.
• 😀 The third example also uses substitution with the system 2x + y = 8 and x - y = 10.
• 😀 In the third example, by substituting y = 10 - x into the first equation, the solution for x is found to be 6 and y equals -4.
• 😀 The video emphasizes the importance of working step-by-step through substitution to find solutions to systems of linear equations.

Q & A

What method is used to solve the system of linear equations in the video?

The substitution method is used to solve the system of linear equations in the video.

What are the two linear equations presented in the first example?

The two linear equations in the first example are: 2x + 3y = 8 and 3x + y = 5.

Why does the speaker prefer to substitute equation 2 into equation 1 in the first example?

The speaker prefers to substitute equation 2 into equation 1 because it involves fewer constants, making it easier to solve.

In the first example, after substitution, what equation is derived?

After substitution, the equation 2x + 3(5 - 3x) = 8 is derived.

How do you simplify the equation 2x + 3(5 - 3x) = 8?

First, distribute the 3 to get 2x + 15 - 9x = 8, then combine like terms to get -7x + 15 = 8.

What is the value of x in the first example?

The value of x is 1 in the first example.

After finding x = 1 in the first example, how is y calculated?

Substitute x = 1 into the equation y = 5 - 3x. This gives y = 5 - 3(1), so y = 2.

In the second example, what are the two linear equations presented?

The two linear equations in the second example are: x + 2y = 1 and 3x - y = 10.

What value of x is obtained in the second example?

The value of x is 3 in the second example.

How does the speaker solve for y in the second example?

The speaker substitutes x = 1 - 2y into the second equation, and after simplifying, finds y = -1.

In the third example, what are the two equations to be solved?

The two equations in the third example are: 2x + y = 8 and x - y = 10.

What is the final solution for x and y in the third example?

The final solution in the third example is x = 6 and y = -4.