How many solution sets do systems of linear inequalities have? Do solutions to systems of linear inequalities need to satisfy both inequalities? In what case might they not?

There can be an infinite number of solutions to a linear inequality. The only real case where there is one solution is when the inequality has two cases and they are both and such as: x ≤ 3 AND x ≥ 3. In this inequality there is only one answer and that answer is 3. Solutions to systems of linear inequalities usually need to satisfy the condition of both inequalities if they are connected by an

AND. In cases where they only need to satisfy one of the inequalities is when they are connected by an OR. For instance in the case x < 3 OR x > 2, there is any number of solutions to this problem. In fact in that particular problem any real number would satisfy the conditions of the line graph. In the equation x < 2 AND x > 3, there is no real solutions because no number can satisfy the conditions of both inequalities.

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