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Question about Inequalities and Equations

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.

Solution Preview

The graphs are in the Word document and are also attached separately.

1.) A system of linear equations has one solution set. The solution set is the group of points that satisfies both inequalities. There can be many points that satisfy both inequalities, and the group of those points is called a solution set.

For example, look at the system of inequalities

y > x + 1
y <= -x + 5

The set of points that satisfies both inequalities is the solution set. It is represented by the purple area in the graph below (graph.png). This is the area that is above the red dotted line (y > x + 1) and also below or on the blue solid line (y <= -x + 5).

[see attachment for graph]

Must solutions to systems of linear ...