1.) How many solution sets do systems of linear inequalities have? Must solutions to systems of linear inequalities satisfy both inequalities? In what case might they not? Provide an example and a reference.
2.) Do the equations x = 4y + 1 and x = 4y - 1 have the same solution? How might you explain your answer to someone who has not learned algebra? Show your work and provide a reference.
Please use your own examples.