SPLTV #Part 4 // Metode Gabungan // Sistem Persamaan Linear Tiga Variabel

Summary

In this educational video, the presenter demonstrates how to solve a system of three-variable linear equations using a combined method of elimination and substitution. Step-by-step, the viewer is guided through eliminating variables and simplifying equations to eventually find the solution: x = 5, y = 3, and z = 7. The video explains the process clearly, starting with elimination between equations, then moving on to substitution for solving the system. This approach is ideal for students learning to tackle systems of equations effectively.

Takeaways

• 😀 The video introduces the combined method of solving linear equations with three variables, using both elimination and substitution methods.
• 😀 The equations given in the script are: x - 2y + z = 6, 3x + y - 2z = 4, and 7x - 6y - z = 10.
• 😀 The first step involves eliminating one variable (in this case, z) by manipulating the equations.
• 😀 To eliminate z, the first equation is multiplied by -2, and the second equation remains the same. This leads to a new equation with two variables, x and y.
• 😀 The script continues with eliminating x by combining the first and third equations, resulting in a new equation with only variables x and y.
• 😀 The fifth equation, resulting from combining the previous ones, has variables x and y, which allows further simplification.
• 😀 The next step involves eliminating y by combining equations with matching coefficients of y, producing a simpler equation.
• 😀 With the new equation, solving for x yields the value x = 5.
• 😀 The value of x = 5 is substituted back into the previous equations, first into equation 4, to solve for y, yielding y = 3.
• 😀 Finally, with both x = 5 and y = 3, the values are substituted into one of the original equations (equation 1) to find z, which equals 7.
• 😀 The final solution to the system of equations is x = 5, y = 3, and z = 7. This is the complete solution set, and the method of combined elimination and substitution is successfully demonstrated.

Q & A

What is the main focus of this video?

The video focuses on explaining the method of solving a system of three linear equations in three variables using a combined approach of elimination and substitution.

What methods were discussed in previous videos before the combined method?

In previous videos, the methods of elimination and substitution were discussed separately.

How does the process of elimination work in the context of the given equations?

In the video, elimination is used to eliminate one of the variables by manipulating the coefficients of the variables. For example, multiplying the equations by appropriate factors to match the coefficients, allowing for the cancellation of a variable when the equations are subtracted.

What are the three given equations in the video?

The three given equations are: 1) x - 2y + z = 6 2) 3x + y - 2z = 4 3) 7x - 6y - z = 10.

Why does the presenter choose to eliminate the variable 'z' first?

The presenter eliminates 'z' first because the coefficients of 'z' in the first two equations are easy to manipulate, allowing for its cancellation and simplifying the system.

What happens when the first and second equations are eliminated?

When the first and second equations are eliminated, a new equation in terms of 'x' and 'y' is created, which is referred to as the fourth equation.

How is the fifth equation obtained?

The fifth equation is obtained by eliminating 'z' again, this time using equations 1 and 3. The coefficients of 'x' and 'y' are adjusted, and the resulting equation is simplified.

How does substitution help in finding the solution for the system of equations?

Substitution is used to replace the variable 'x' in the equations once its value is determined. This helps in finding the value of 'y' and then 'z' in a step-by-step manner.

What is the value of 'x' that the presenter calculates?

The value of 'x' calculated by the presenter is 5.

How is the final solution for 'y' determined?

The value of 'y' is determined by substituting 'x = 5' into one of the simplified equations. The result is that 'y' equals 3.

What is the final value of 'z'?

The final value of 'z' is found to be 7 by substituting the values of 'x' and 'y' into one of the original equations.