# System of equations with 3 variables. | Summary and Q&A

4.8K views
September 14, 2016
by
blackpenredpen
System of equations with 3 variables.

## TL;DR

This video explains how to solve a 3X3 system of equations by applying the elimination method, emphasizing the importance of organizing work and exercising patience.

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### Q: What is the significance of choosing which variable to eliminate first in solving a 3X3 system of equations?

The choice of variable to eliminate first determines the order in which the equations are combined later on. It affects the simplicity and efficiency of the solution process.

### Q: How is the LCM used to make the numbers in front of the chosen variable the same?

The LCM is calculated for the coefficients of the chosen variable, and then the equations are multiplied by the necessary factors (positive or negative) to achieve this common multiple.

### Q: Why should the signs in front of the variables alternate when making the numbers the same?

Alternating signs ensure that the coefficients of the chosen variable are in the desired pattern, simplifying the combination of equations later on.

### Q: Why is it necessary to solve the resulting 2X2 system of equations after eliminating one variable?

Solving the resulting 2X2 system of equations narrows down the solutions and provides the values for the remaining variables.

## Summary & Key Takeaways

• The video demonstrates the step-by-step process of solving a 3X3 system of equations using the elimination method.

• It emphasizes the need to organize work and choose which variable to eliminate first.

• LCM (Least Common Multiple) is used to make the numbers in front of the chosen variable the same.

• The equations are combined, eliminating the chosen variable, until a 2X2 system of equations is obtained.