Sistem persamaan linear dua variabel kelas 10 - metode grafik

Summary

In this lesson, we explore the system of linear equations with two variables (SPLDV). The script explains the concept using two linear equations: 2x - y = 2 and 4x + 2y = 20. Several methods for solving SPLDV are discussed, including the graphical method. By plotting the coordinates for each equation on a graph, the intersection point (3, 4) is identified as the solution. The explanation is clear and detailed, helping students understand how to solve systems of linear equations visually.

Takeaways

• 😀 SPLDV stands for 'System of Linear Equations of Two Variables', consisting of linear equations with two variables.
• 😀 The system is called linear because the highest power of variables (x and y) is 1.
• 😀 The two variables in SPLDV are typically denoted as x and y.
• 😀 There are four methods to solve SPLDV: graphical, elimination, substitution, and mixed methods.
• 😀 The graphical method involves plotting the equations on a graph and finding the intersection point.
• 😀 In the graphical method, you first find the coordinates for each equation by substituting values for x and y.
• 😀 For the first equation (2x - y = 2), setting x = 0 gives y = -2, and setting y = 0 gives x = 1.
• 😀 For the second equation (4x + 2y = 20), setting x = 0 gives y = 10, and setting y = 0 gives x = 5.
• 😀 Plotting these points on a graph helps visualize the solution to the system of equations.
• 😀 The solution to the system is the point where the two lines intersect on the graph, which in this case is (3, 4).

Q & A

What is SPLDV?

SPLDV stands for 'System of Linear Equations in Two Variables,' which involves solving systems consisting of multiple linear equations, each with two variables, typically denoted as x and y.

Why is the system called a 'linear equation'?

The system is called a 'linear equation' because the highest power of the variables (x and y) is 1, making the equations linear in nature.

What are the two equations given in the example of SPLDV?

The two equations in the example are: 2x - y = 2 and 4x + 2y = 20.

What is the graphical method in solving SPLDV?

The graphical method involves plotting both equations on a coordinate plane to find the intersection point. This intersection point represents the solution to the system of equations.

How do we find the coordinates for the first equation in the graphical method?

To find the coordinates for the first equation 2x - y = 2, substitute values for x (such as 0 and 1), solve for y, and obtain the corresponding coordinates.

What are the coordinates for the first equation 2x - y = 2?

For the first equation, the coordinates are (0, -2) when x = 0, and (1, 0) when y = 0.

How do we find the coordinates for the second equation in the graphical method?

To find the coordinates for the second equation 4x + 2y = 20, substitute values for x (such as 0 and 5), solve for y, and obtain the corresponding coordinates.

What are the coordinates for the second equation 4x + 2y = 20?

For the second equation, the coordinates are (0, 10) when x = 0, and (5, 0) when y = 0.

What is the importance of graphing the points in the graphical method?

Graphing the points is important because it visually shows the relationship between the equations, and the intersection of the two lines represents the solution to the system.

What is the solution to the system of equations 2x - y = 2 and 4x + 2y = 20?

The solution to the system is the point where the two lines intersect on the graph, which is (x, y) = (3, 4).