Understanding Systems of Equations

The video tutorial explains how to solve a system of three equations with three unknowns using the method of elimination. It discusses the possible outcomes: one solution, no solution, or infinite solutions. The tutorial demonstrates labeling equations, eliminating variables, and solving the system. It highlights the case of infinite solutions and how to express them using a parameter T. The video concludes with a graphical verification of the infinite solutions, showing the intersection of planes in space.

What are the possible outcomes when solving a system of three equations using the method of elimination?

• Only infinite solutions

• Only no solution

• Only one solution

• One solution, no solution, or infinite solutions

Why is it beneficial to label equations when solving a system?

• To confuse the solver

• To keep the process organized

• To avoid solving the system

• To make the equations look more complex

What is the result when adding equations A and B in this system?

• 3x - 2z = 0

• 2x + 2z = 0

• x - z = 0

• 3x + 2z = 0

What does the equation 0 = 0 indicate about the system of equations?

• The system has no solution

• The system has one solution

• The system has infinite solutions

• The system is inconsistent

How can infinite solutions be expressed in terms of a new variable?

• By using only fractions

• By using only integers

• By using a new variable like T

• By using a constant value

If z is expressed as T, what is the expression for x?

• x = 5/3T

• x = 3/2T

• x = 2/3T

• x = T

How do you express y in terms of T using equation B?

• y = 2/3T

• y = T

• y = 3/2T

• y = 5/3T

What does the graphical representation of the system show?

• The planes do not intersect

• The planes intersect at a single point

• The planes intersect along a line

• The planes are parallel

What does the intersection of three planes along a line indicate?

• The system is inconsistent

• There are infinite solutions

• There is a unique solution

• There is no solution

What is the significance of expressing solutions as a motor triple in terms of T?

• It provides a single solution

• It shows the relationship among variables

• It simplifies the system

• It eliminates the need for a graph