Solving Systems of Equations

The video tutorial demonstrates solving a system of three equations with three unknowns using the elimination method. It begins by labeling the equations and focuses on eliminating the Z terms to simplify the system. The tutorial then solves for X and Y using elimination and finds Z through back substitution. Finally, it visualizes the solution by graphing the planes and concludes with a summary of the solution.

What is the main method used to solve the system of equations in this tutorial?

• Elimination

• Graphing

• Matrix Inversion

• Substitution

Why is it beneficial that equation C contains only two variables?

• It makes substitution straightforward.

• It reduces the number of equations needed.

• It allows for easier elimination of Z terms.

• It simplifies the graphing process.

What operation is performed on equation A to help eliminate the Z terms?

• It is added to equation C.

• It is divided by 2.

• It is squared.

• It is multiplied by -1.

After eliminating the Z terms, what is the new equation formed?

• X - Y = 5

• X + Y = 0

• -2X + 7Y = 9

• 3X - 8Y = 14

What is the next step after forming equations C and D?

• Solve for Z using substitution.

• Graph the equations.

• Eliminate the X terms.

• Check for consistency.

What is the value of Y after solving the system of equations C and D?

• 2

• -1

• 1

• 0

Which equation is used to find the value of Z?

• Equation C

• Equation B

• Equation D

• Equation A

What is the final value of Z in the solution?

• 0

• 3

• -1

• -3

How is the solution to the system of equations represented?

• As an ordered triple

• As an ordered pair

• As a line

• As a single point

What does the graphical representation of the solution show?

• The intersection of two lines

• The intersection of three planes

• The intersection of a line and a plane

• The intersection of four planes