#29. Solving a System of Linear Equations with Three Variables Algebra Problem

TL;DR

By adding and canceling variables, we can solve a system of equations to find the values of X, Y, and Z.

Transcript

problem number 29 by hand find the solution set for the following system so we have a system of equations so we have X plus 3y minus 4z equals negative 3 and then we have 2x minus 2y plus 4z equals 10 and the last equation is 2x minus 4y plus 4z equals 14 and the goal here is to find XY and Z as well so there's lots of ways to do this I'm noticing ... Read More

Key Insights

• ❓ There are multiple methods to solve a system of equations, but this content focuses on using addition and cancellation to simplify equations.
• 🤪 By adding the first two equations and the first and last equations, the Z variable cancels out in both cases.
• ❓ The remaining equations can then be solved to find the values of X and Y.
• ☺️ The value of Z can be obtained by substituting the known values of X and Y into any of the original equations.
• 😥 The solution to the system of equations is represented as an ordered point in three-dimensional space.

Questions & Answers

Q: What is the goal when solving a system of equations?

The goal is to eliminate a variable and obtain a simplified equation with two variables.

Q: How do you solve a system of equations when canceling out variables?

By adding equations to eliminate the same variable, you can simplify the system and solve for the remaining variables.

Q: How can you find the value of X in a system of equations?

You can divide the resulting coefficient of X by the sum of its coefficients to find the value of X.

Q: What is back substitution?

Back substitution involves substituting the value of one known variable into an equation to solve for another unknown variable.

Summary & Key Takeaways

• The content demonstrates how to solve a system of equations with three variables (X, Y, and Z) by adding and canceling variables.

• By adding the first two equations and the first and last equations, the Z variable cancels out.

• The resulting equations can be solved to find the values of X, Y, and Z.