Understanding Systems of Equations

The video tutorial explains how to determine if a system of equations is inconsistent or dependent. It covers labeling equations, possible outcomes, and solving systems using the method of elimination. The tutorial demonstrates how to find infinite solutions and express variables x and y as functions of t, showing the relationship among x, y, and z.

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

• No 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 infinite solutions

What does it mean if a system of equations is inconsistent?

• The system has two solutions

• The system has no solution

• The system has one solution

• The system has infinite solutions

Which equations are used to eliminate the y terms in the method of elimination?

• Equations a and b

• Equations b and c

• Equations b and d

• Equations a and c

What is the result of adding equations a and 3 times equation c?

• Negative 7x plus 21z equals 77

• 7x plus 21z equals 77

• Negative 7x minus 21z equals 77

• 7x minus 21z equals 77

What does zero equals zero indicate about the system?

• The system has no solution

• The system has one solution

• The system has infinite solutions

• The system is inconsistent

How is x expressed as a function of t?

• x = -11 + 3t

• x = 11 + 3t

• x = 11 - 3t

• x = -11 - 3t

Which equation is used to express y as a function of t?

• Equation d

• Equation b

• Equation c

• Equation a

What is the expression for y in terms of t?

• y = -5t + 18

• y = -18 + 5t

• y = -5t - 18

• y = 18 - 5t

What is the significance of expressing the solution as an ordered triple?

• It shows the relationship among x, y, and z

• It eliminates the need for equations

• It simplifies the solution

• It provides a unique solution

What is the z-coordinate in the ordered triple?

• z = t

• z = -t

• z = 1

• z = 0