Solving Systems of Equations with Three Variables

The video tutorial explains how to solve systems of three-variable equations algebraically. It covers the different types of solutions: one solution, infinite solutions, and no solution. The tutorial provides step-by-step examples for each type, demonstrating the use of elimination and substitution methods. It concludes with a practice section for solving 3x3 systems.

What does it mean when three planes intersect at one point in a three-variable system?

• The system's solution cannot be determined

• The system has no solution

• The system has infinite solutions

• The system has exactly one solution

How do you typically start solving a system of three variable equations?

• By graphical plotting

• By substitution

• By elimination

• By matrix operations

What does the equation '0 = 2' indicate about the system of equations?

• The system needs re-evaluation

• The system has infinite solutions

• The system has no solution

• The system has one solution

What is the result of adding two equations where the variable Z is eliminated?

• An equation in X and Y

• No equation can be formed

• An equation in X and Z

• An equation in Y and Z

After eliminating Z, what method is used to solve for X or Y?

• Matrix method

• Graphical method

• Substitution method

• Elimination method

When solving for Y, what does the equation '-18y = -72' simplify to?

• y = -4

• y = 4

• y = 18

• y = -18

What happens when you get inconsistent Y values in different equations?

• It indicates no solution

• It indicates that further calculation is needed

• It indicates one solution

• It indicates infinite solutions

What is the outcome when the planes do not intersect at any point?

• The outcome is undetermined

• Infinite solutions

• No solution

• One solution

In the context of three-variable systems, what does the equation '0 = 0' suggest?

• No solution

• Infinite solutions

• Exactly one solution

• The equation is invalid

What does a consistent equation like '0 = 0' imply in a three-variable system?

• The system has no solution

• The system's equations are incorrect

• The system has exactly one solution

• The system has infinite solutions