Graph the solution set of each system of inequalities. { y ...

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Key Concepts

Graphing Linear Inequalities

Graphing linear inequalities involves first graphing the corresponding equality of the inequality (i.e., plotting the line). Once the line is drawn—using a solid line if the inequality includes equality (? or ?) or a dashed line if not—the next step is to determine which side of the line represents the solution set. This is typically done by selecting a test point not on the line and substituting it into the inequality; if the inequality holds, the half-plane that contains the test point is shaded to represent all solutions.

Feasible Region

The feasible region in the context of a system of inequalities is the set of all points that simultaneously satisfy all the inequalities in the system. This region is found by graphing each inequality individually and then identifying the area where their shaded regions overlap. It represents the solution set of the entire system.

Systems of Linear Inequalities

A system of linear inequalities consists of two or more inequalities that define constraints on the variables. The solution process involves graphing each inequality to represent their respective constraints, and then finding the intersection of these graphs, which yields the set of all possible solutions that satisfy every inequality in the system.

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