Solving Systems of Equations

The video tutorial explains how to solve a system of three equations with three unknowns. It highlights the unique structure of the system, where each equation has a different number of variables. The tutorial demonstrates solving the system by substitution, starting with the known value of z, then finding y, and finally solving for x. The solution is verified graphically by showing the intersection point of three planes, confirming the ordered triple (-4, 0, 1) as the solution.

What are the possible types of solutions for a system of equations with three unknowns?

• One solution, two solutions, or infinite solutions

• One solution, no solution, or infinite solutions

• Two solutions, no solution, or infinite solutions

• One solution, two solutions, or no solution

What is the form of the solution if there is one solution for the system of equations?

• A matrix

• An ordered triple

• A single number

• An ordered pair

What is the value of the z-coordinate in the solution of the given system?

• 1

• 3

• 0

• 2

How do we find the value of y in the system of equations?

• By substituting the value of z

• By substituting the value of both x and z

• By solving the first equation directly

• By substituting the value of x

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

• 1

• 2

• 0

• 3

Which equation is used to solve for x after finding y and z?

• The second equation

• None of the equations

• The third equation

• The first equation

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

• -4

• 0

• 1

• 5

What does the graphical representation of the solution show?

• The solution is a line

• The solution is incorrect

• The solution is a point on all three planes

• The solution is a plane

What is the ordered triple solution of the system of equations?

• (0, 1, -4)

• (-4, 0, 1)

• (1, 0, -4)

• (0, -4, 1)