Simultaneous Equations Three Variables Using Elimination - Math lesson

TL;DR

This video explains how to solve simultaneous equations with three variables using the elimination method.

Transcript

good day welcome to the techmath channel I'm Josh in this video we're going to be using the elimination method to solve simultaneous equations that involve three variables so ones like you can see here we have three equations and they have three variables x y and Zed and the way we're going to do this is as follows we're going to by combining reduc... Read More

Key Insights

• ❓ The elimination method is a systematic approach to solving simultaneous equations with multiple variables.
• ⌛ By combining equations, it is possible to eliminate one variable at a time and reduce the number of variables involved in the equations.
• 👻 The reduction of equations allows for a simpler solution process and makes it easier to find the values of the variables.
• ⚾ It is important to carefully select which equations to combine based on opposite coefficients for a specific variable.
• 🔨 The elimination method is a valuable tool for solving complex systems of equations efficiently.
• ⏫ It is crucial to double-check the solutions by substituting the values back into the original equations to ensure accuracy.
• 🎮 The step-by-step approach demonstrated in the video provides a clear and easy-to-follow method for solving simultaneous equations with three variables.

Questions & Answers

Q: What is the elimination method used for in solving simultaneous equations?

The elimination method is used to simplify a set of equations by eliminating one variable at a time, making it easier to solve for the remaining variables.

Q: How do you determine which equations to combine in the elimination method?

In the elimination method, you combine equations that have opposite coefficients for one of the variables. By doing this, the variable cancels out when the equations are added.

Q: What is the purpose of reducing three equations to two equations in the elimination method?

By reducing three equations to two equations, you eliminate one variable and obtain equations with only two variables. This simplification allows you to solve for the remaining variables more easily.

Q: How do you find the values of X, Y, and Z after reducing the equations?

After reducing the equations, you solve for one variable (in this case, X), substitute its value back into one of the equations to find the value of another variable (Y), and finally substitute the values of X and Y to solve for the remaining variable (Z).

Summary & Key Takeaways

• The video demonstrates how to reduce three equations with three variables down to two equations with two variables using the elimination method.

• The first step involves combining two equations to eliminate one variable and obtain equations with only X and Y.

• The second step is to combine different equations to eliminate another variable and obtain two equations with X and Y.

• The final step is to eliminate the remaining variable, solve for X, and substitute the values back into one of the original equations to find the values of Y and Z.