How Many Solution Sets Do Systems of Linear Inequalities Have?

How Many Solution Sets Do Systems of Linear Inequalities Have?

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.

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.