Understanding Systems of Equations in Three Variables

This video tutorial introduces solving systems of equations in three variables, explaining the possible outcomes: a single solution, infinite solutions, or no solution. It details the algebraic method for solving these systems using elimination and substitution, and provides a step-by-step example. The video concludes with a preview of additional examples in the next part.

What does a linear equation in three variables represent in 3D space?

• A line

• A point

• A plane

• A cube

What is the result when three planes intersect at a single point?

• The system is inconsistent

• The system has infinite solutions

• The system has no solution

• The system has one solution

If three planes intersect along a line, what can be said about the system?

• It has one solution

• It is inconsistent

• It has infinite solutions

• It has no solution

What is the first step in solving a system of equations in three variables using the elimination method?

• Substitute values

• Select two equations and eliminate one variable

• Graph the equations

• Solve for one variable

What should you do after eliminating one variable from two different pairs of equations?

• Solve the resulting system of two equations

• Graph the remaining equations

• Check for consistency

• Substitute the eliminated variable back

In the example provided, what is the value of Z in the solution?

• 1

• 0

• 3

• 2

What is the final step in finding the solution to the system of equations in the example?

• Graph the solution

• Eliminate another variable

• Find the value of X using one of the original equations

• Verify the solution

Why is it important to label each equation when solving systems of equations?

• To avoid using the wrong method

• To keep track of the steps

• To simplify the equations

• To make the process faster

What does the graphical representation of the solution show?

• No intersection

• The intersection of three planes along a line

• The intersection of three planes at a point

• The intersection of two planes

What will be covered in the next video?

• Applications of systems of equations

• A review of the current method

• A new method for solving equations

• More examples with no solution and infinite solutions