Sistem Persamaan Linier Dua Variabel (SPLDV) Metode SUBTITUSI

Batam Update
27 Sept 202011:41

Summary

TLDRIn 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.

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