A system of equations that has at least one solution is called consistent. A system of equations that has no solutions is called inconsistent. A system with infinitely many solutions is called dependent. A system of equations that has exactly one solution is called independent. Follow the steps in 14a-g to make some discoveries about inconsistent and dependent systems.
a. Graph each of the following systems of linear equations. Use your graphs to identify each system as consistent, inconsistent, dependent, and/or independent.
i.


ii.


iii.


iv.


v.


vi.


vii.


viii.


ix.


b. Describe the graphs of the equations of the inconsistent systems.
c. Try to solve each inconsistent system by substitution or by elimination. Show your steps. Describe the outcome of your attempts.
d. How can you recognize an inconsistent linear system without graphing it?
e. Describe the graphs of equations of consistent and dependent systems.
f. Try to solve each consistent and dependent system by substitution or by elimination. Show your steps.
Describe the outcome of your attempt.
g. How can you recognize a consistent and dependent linear system without graphing it?