Consistent and Inconsistent Systems

When a system of two linear equations has one solution it means that...

• The lines are the same line and every point on the line is a solution
• The two lines meet or "intersect" at one point
• The lines are parallel to each other

In a consistent dependent system...

• There are infinitely many solutions
• There's only one solution
• There's not solution
• There are one solution or infinitely many solutions

In a consistent independent system...

• There's no solution
• There's one solution or infinitely many solutions
• There are infinitely many solutions
• There's only one solution

In an inconsistent system of linear equations...

• The lines are parallel to each other and there's one solution
• The lines are parallel to each other and there are infinitely many solutions. 
• The lines are parallel to each other and there's no solution
• The lines are perpendicular to each other and they meet at one point

An inconsistent system of linear equations happens when...

• There's only one solution to the system
• There's no solution to the system
• There are infinitely many solutions to the system.
• There are one or infinitely many solutions to the system

A consistent system of linear equations happens when...

• There are one or infinitely many solutions to a system
• There's only one solution to the system
• There's no solution to the system
• There's an infinite number of solutions to a system

Consistent or Inconsistent?

• Consistent
• Inconsistent

Dependent or Independent?

• Dependent
• Independent
• Neither

WITHOUT GRAPHING
what can you say about these lines

• Consistent and Dependent
• Consistent and Independent
• Inconsistent and Dependent
• Inconsistent and Independent

WITHOUT GRAPHING
what can you say about these lines

• Consistent and Dependent
• Consistent and Independent
• Neither
• Inconsistent