Sistem Persamaan Linear Dua Variabel | Matematika | SayaBisa

Summary

This video explains linear equations with two variables (PLDV) and their application in solving systems of linear equations (SPLDV). It covers the graphical method, where two linear equations are plotted by finding their x and y intercepts. By drawing the lines, the point of intersection reveals the solution to the system. In this case, the solution is x = 3 and y = 1. The video demonstrates how SPLDV is used to solve for variable values and how different methods, including graphical, substitution, elimination, and mixed approaches, can be applied.

Takeaways

• 😀 Linear equations form straight lines on a graph, meaning they create straight-line graphs.
• 😀 A linear equation with two variables is called a 'persamaan linear dua variabel' (PLDV) or two-variable linear equation.
• 😀 In the previous section, the straight-line equation (PGL) was also a two-variable linear equation (PLDV).
• 😀 The essential characteristic of a PLDV is that it has two variables, neither of which are raised to a power.
• 😀 SPLDV stands for 'Sistem Persamaan Linear Dua Variabel', which means a system of two linear equations.
• 😀 SPLDV is used to solve for the values of variables (x and y) in a system of two equations.
• 😀 There are four methods to solve SPLDV: graphical method, substitution, elimination, and a combination of methods.
• 😀 The video focuses on solving SPLDV using the graphical method, which involves plotting two equations on a graph.
• 😀 To graph a linear equation, find the x- and y-intercepts. For example, if y = 0, the x-intercept is found by solving for x; similarly for the y-intercept.
• 😀 After finding the intercepts of both equations, plot them on the graph and draw straight lines to find the point of intersection, which gives the solution for x and y.
• 😀 After plotting both equations on the graph, the point of intersection represents the solution, and this can be checked by substituting the values of x and y back into the original equations to confirm the accuracy.

Q & A

What is a linear equation?

A linear equation is an equation that forms a straight line. The key characteristic is that the variables involved are not raised to any power.

What is a two-variable linear equation?

A two-variable linear equation (PLDV) is an equation that involves two variables, each with no exponents, and the equation forms a straight line when graphed.

What does the acronym 'PLDV' stand for?

PLDV stands for 'Persamaan Linear Dua Variabel', which translates to 'Two-variable Linear Equation' in English.

What is the meaning of 'SPLDV'?

SPLDV stands for 'Sistem Persamaan Linear Dua Variabel', which refers to a system of two linear equations with two variables. It is used to find the values of the variables that satisfy both equations.

What is the main goal of solving a system of two linear equations (SPLDV)?

The goal is to find the values of the variables (typically x and y) that satisfy both equations in the system.

What are the methods used to solve SPLDV?

The four main methods for solving SPLDV are graphical, substitution, elimination, and a combination of these methods.

How do you graphically solve SPLDV?

To solve SPLDV graphically, you first plot the two equations by finding their x- and y-intercepts. Then, draw the lines for each equation and find their intersection point, which gives the values of the variables.

What is the process to find the intercepts of a linear equation?

To find the intercepts, set y = 0 to find the x-intercept, and set x = 0 to find the y-intercept.

In the example, what are the intercepts of the first equation?

For the first equation, the x-intercept is (4, 0), and the y-intercept is (0, 4).

What is the solution to the system of equations in the example?

The solution to the system is x = 3 and y = 1, as determined by the point where the two lines intersect.