The video tutorial covers solving systems of linear equations in three variables. It begins with testing if a given order triple is a solution to the system. The instructor then demonstrates solving the system using the elimination method, focusing on eliminating variables to find solutions. The tutorial concludes with a final problem, reinforcing the concepts taught.

What is the main focus of this video tutorial?

• Factoring polynomials

• Graphing linear equations

• Solving systems of linear equations in three variables

• Solving quadratic equations

What is the first step in determining if an ordered triple is a solution?

• Graphing the equations

• Substituting the values into the equations

• Solving for one variable

• Eliminating a variable

If one equation does not hold true after substitution, what can be concluded about the ordered triple?

• It needs further testing

• It is a partial solution

• It is not a solution

• It is a solution

What method is introduced for solving systems of equations?

• Graphing method

• Matrix method

• Substitution method

• Elimination method

Which variable is chosen to be eliminated first in the example?

• None

• X

• Y

• Z

After eliminating Z, what is the value of X found to be?

• 2

• 1

• 3

• 4

What is the next step after finding the value of X?

• Solve for Y

• Solve for Z

• Verify the solution

• Graph the equations

How is the solution verified?

• By substituting back into the original equations

• By graphing the equations

• By using a calculator

• By checking with a different method

In the final problem, which variable is chosen to be eliminated first?

• X

• None

• Y

• Z

What is the final ordered triple solution for the last system of equations?

• (1, 5, 6)

• (3, 1, -2)

• (2, 4, 5)

• (0, 0, 0)