Solving Systems of Equations Using Elimination

The video tutorial explains how to solve a system of three equations with three unknowns using the method of elimination. It covers the process of eliminating variables to reduce the system to two equations, solving for the unknowns, and verifying the solution. The tutorial demonstrates the steps to eliminate the Z terms from pairs of equations, solve the reduced system, and perform back substitution to find the final solution. The solution is verified by graphing the planes and confirming the intersection point.

What are the possible outcomes when solving a system of three equations with three unknowns?

• One solution, two solutions, or infinite solutions

• No solution, two solutions, or infinite solutions

• Two solutions, no solution, or infinite solutions

• One solution, no solution, or infinite solutions

What is the first step in the elimination method for solving systems of equations?

• Solving for one variable

• Selecting two equations to eliminate a variable

• Substituting values

• Graphing the equations

How do you eliminate the Z terms from equations A and B?

• Multiply equation A by 2

• Multiply equation B by 3

• Subtract equation B from equation A

• Add equations A and B directly

What is the result of adding equations A and B after eliminating the Z terms?

• Equation C

• Equation F

• Equation E

• Equation D

What is the purpose of multiplying equation B by negative two in the elimination process?

• To eliminate the Y terms

• To simplify the equation

• To make the Z terms opposites

• To eliminate the X terms

After eliminating the Z terms from equations B and C, what is the resulting equation called?

• Equation F

• Equation E

• Equation G

• Equation D

What is the next step after obtaining equations D and E?

• Solve for Z

• Check for consistency

• Solve as a system of two equations with two unknowns

• Graph the equations

How do you eliminate the Y terms in the system of two equations?

• Multiply equation D by 4

• Multiply equation E by 4

• Add equations D and E directly

• Subtract equation E from equation D

What is the value of X in the solution of the system?

• 0

• 2

• 1

• -1

What is the final solution of the system in ordered triple form?

• (0, 0, 1)

• (0, 1, 0)

• (1, 1, 1)

• (1, 0, 0)