Q:

# How many solution sets do systems of linear inequalities have?

A:

Linear inequalities can either have no solution, one specific solution, or an infinite amount of solutions. Thus, the total possible would equal three. In order for a number to be a solution to a linear inequality, it must satisfy all linear inequalities.

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For example, in a system with two linear inequalities:

- No solution: x>7 and x<4 because a number cannot be greater than 7 and less than 4.

- One solution: x>=7 and x<=7 because the only value that satisfies both inequalities is 7.

- Infinite number of solutions: x>1 and x>2 because all numbers greater than 2 satisfy both inequalities.

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