Cara Cepat Menghitung Sistem Persamaan Linear Dua Variabel (SPLDV)

Summary

This tutorial demonstrates how to quickly solve a system of two-variable linear equations using elimination. The example involves solving the equations 4x + 7y = 2 and 3x + 2y = -5. The method focuses on eliminating one variable by manipulating the equations, ultimately leading to the solution of x = -3 and y = 2. The tutorial guides the viewer through each step clearly, offering a visual and step-by-step breakdown to ensure easy understanding of the elimination technique.

Takeaways

• 😀 The video explains how to quickly solve a system of linear equations with two variables.
• 😀 The given system of equations to solve is: 4x + 7y = 2 and 3x + 2y = -5.
• 😀 The first step involves writing down the equations clearly before beginning the solution process.
• 😀 To solve for x, the method used involves eliminating the variable y by multiplying both equations.
• 😀 The equations are modified to align the coefficients of y for easy elimination: 2(4x + 7y) = 4 and 7(3x + 2y) = -35.
• 😀 After multiplying and adjusting the equations, they are subtracted to eliminate the variable y.
• 😀 The subtraction results in an equation that allows solving for x, giving x = -3.
• 😀 After determining x, the next step is to substitute x = -3 into one of the original equations to solve for y.
• 😀 Substituting x = -3 into the first equation, we get y = 2.
• 😀 The solution set is (x, y) = (-3, 2), which is the final answer.
• 😀 The video concludes by encouraging viewers to try solving similar problems on their own and wishing them success.

Q & A

What is the method being demonstrated in the video?

The video demonstrates a quick method for solving a system of linear equations with two variables.

What are the two equations in the system being solved?

The system consists of the equations: 4x + 7y = 2 and 3x + 2y = -5.

What is the first step in solving the system of equations?

The first step is to write down the two equations clearly for reference.

How is the variable y handled in the solution process?

In the first step, the variable y is isolated, and the equation is manipulated to eliminate y by multiplying both sides by appropriate values.

What is the significance of the colored lines in the video?

The colored lines (blue and red) are used to highlight different steps in the multiplication and subtraction process, making it easier to follow the logic.

How do you find the value of x in this method?

To find x, the first step involves eliminating y by multiplying the coefficients and then subtracting the resulting values from both sides.

What happens after finding the value of x?

Once the value of x is found, the next step is to substitute this value back into one of the original equations to find y.

What is the final value of x in the system of equations?

The final value of x is -3.

What is the value of y after solving the system?

The value of y is 2 after solving the system.

What is the solution to the system of equations?

The solution to the system of equations is x = -3 and y = 2, which is the solution set (-3, 2).