Dependent and Inconsistent Systems of Equations

The video tutorial explores different types of systems of equations, including consistent, inconsistent, and dependent systems. It demonstrates how to solve these systems using elimination and substitution methods. Consistent systems have a single solution, inconsistent systems have no solution due to parallel lines, and dependent systems have infinite solutions as they represent the same line.

What is the solution to a consistent system of equations?

• Two solutions

• Exactly one solution

• Infinite solutions

• No solution

In a consistent system, what does the intersection of lines represent?

• No intersection

• Infinite intersections

• Parallel lines

• A single point

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

• The equations have infinite solutions

• The equations have no solution

• The equations are identical

• The equations have a single solution

What characteristic do the lines of an inconsistent system share?

• They intersect at one point

• They are parallel

• They overlap completely

• They are perpendicular

What is the slope of the lines in an inconsistent system?

• Zero slope

• Negative slope

• Same slope

• Different slopes

How can you identify a dependent system of equations?

• The equations have no solution

• The equations have a single solution

• The equations are identical or multiples of each other

• The equations are perpendicular

What is the graphical representation of a dependent system?

• Two intersecting lines

• Two parallel lines

• Two perpendicular lines

• A single line

What does it mean if two equations are dependent?

• They have infinite solutions

• They have exactly one solution

• They are perpendicular

• They have no solutions

Which type of system results in a statement like 0 = 0?

• Consistent system

• Independent system

• Inconsistent system

• Dependent system

What is the result of solving a dependent system of equations?

• Two solutions

• Infinite solutions

• One solution

• No solution