Solve a 3 by 3 system of equations!

TL;DR

Learn how to solve a system of three equations with three variables using the elimination method.

Transcript

let's solve a 3X3 system of equations by using the elimination method and this is how I would recommend you guys to do it pick a variable that you want eliminate that variable first and to do that let's say I want to eliminate X first then you will have to make sure the number in front of the X are going to be the same and then also you have to mak... Read More

Key Insights

• 💨 The elimination method is an effective way to solve a system of equations when there are three variables involved.
• ❓ Identifying the LCM of the coefficients is crucial for creating equations with the same coefficient for the elimination process.
• 🤘 Alternating signs in the equations help cancel out variables during the elimination process.
• 🔌 Reducing fractions when plugging variables back into equations helps simplify calculations.
• ⌛ The elimination process involves systematically eliminating one variable at a time until you have a 2x2 system of equations.
• 💤 The solution can be written as an ordered triple, with each number representing the values of X, Y, and Z in the system of equations.

Questions & Answers

Q: How do you determine the lowest common multiple (LCM) of the coefficients in a system of equations?

To find the LCM, identify the prime factors of each number and then multiply the highest power of each prime factor. In this case, the LCM is used to create equations with the same coefficient for the variable in the elimination process.

Q: Can you explain why it's important for the signs of the coefficients to alternate when multiplying the equations?

The alternating signs ensure that when the equations are added or subtracted, the coefficients of the variable cancel out. This allows for the elimination of the variable, simplifying the system of equations.

Q: What is the purpose of reducing fractions when plugging variables back into the equations?

Reducing fractions makes calculations easier and keeps the equations simpler. It helps avoid potential errors and allows for a more streamlined solution process.

Q: How do you use the elimination method to solve a 3x3 system of equations?

The elimination method involves systematically eliminating one variable at a time by manipulating the equations. By multiplying equations to create equal coefficients for the targeted variable, you can cancel out the variable and simplify the system until you have a 2x2 system of equations. Repeat the process to solve for all variables.

Summary & Key Takeaways

• Use the elimination method to solve a 3x3 system of equations by eliminating one variable at a time, ensuring the coefficients of the variable are the same and the signs alternate.

• Find the lowest common multiple (LCM) of the coefficients and use it to create equations with the same coefficient for each variable.

• Multiply the equations to eliminate the variable, and repeat the process until you have a 2x2 system of equations.

• Continue eliminating variables until you have solved for all three variables.