The video tutorial explains how to solve a system of three equations with three variables. It begins by introducing the concept and then demonstrates the process of eliminating one variable using two pairs of equations. The tutorial continues by forming two new equations with two variables, solving them to find the values of x and z, and finally substituting these values back into one of the original equations to find the value of the third variable, y. The tutorial emphasizes the importance of choosing the right variable to eliminate and provides tips to avoid common mistakes.

What is the main objective of the video tutorial?

• To explore calculus concepts

• To understand linear functions

• To learn about quadratic equations

• To solve a system of equations with three variables

How many variables are present in the system of equations discussed?

• Four

• Two

• Five

• Three

What is the first step in solving the system of equations?

• Substitute values

• Graph the equations

• Eliminate one variable

• Use matrices

Which variable is chosen to be eliminated first?

• x

• y

• z

• None

Why is 'y' chosen as the variable to eliminate?

• It has a coefficient of 1

• It appears in all equations

• It is the easiest to substitute

• It has the largest coefficient

What operation is performed to eliminate 'y' from the first pair of equations?

• Division

• Addition

• Multiplication

• Subtraction

What is the result of eliminating 'y' from the first pair of equations?

• A new equation with 'x', 'y', and 'z'

• A new equation with 'x' and 'y'

• A new equation with 'y' and 'z'

• A new equation with 'x' and 'z'

What is the next step after forming two new equations without 'y'?

• Solve for 'x' and 'z'

• Substitute back into the original equations

• Check for errors

• Graph the equations

How is the system of two equations solved?

• By graphing

• By substitution or elimination

• By using matrices

• By trial and error

What is the value of 'x' after solving the system of two equations?

• 2

• 0

• -1

• 1