Graphing systems of linear inequalities involves finding the region of the coordinate plane that satisfies all inequalities simultaneously. Each inequality represents a half-plane, and the solution to the system is the intersection of these half-planes. The boundary line of each inequality is solid if the inequality includes "equal to" ($\leq$ or $\geq$) and dashed if it does not ($<$ or $>$). The solution region is shaded to indicate all points that satisfy every inequality in the system.
To graph a system, first graph each inequality individually. Then, identify the region where all shaded areas overlap. This overlapping region represents the solution set of the system. Points within this region, and on solid boundary lines, are solutions to the system of inequalities.
Match the term with its definition:
| Term | Definition |
|---|---|
| 1. Boundary Line | A. The region where all inequalities are satisfied. |
| 2. Half-Plane | B. A line that divides the coordinate plane into two regions. |
| 3. System of Inequalities | C. A set of two or more inequalities considered together. |
| 4. Solution Region | D. The line that represents the equality form of an inequality. |
| 5. Dashed Line | E. Indicates the boundary line is not included in the solution. |
A system of linear inequalities is a set of two or more linear ________ considered together. To solve a system of linear inequalities, you must graph each ________ individually. The solution to the system is the ________ of the shaded regions. If the inequality includes "equal to", the boundary line is ________; otherwise, it is ________.
Explain why a point on a dashed boundary line is not included in the solution set of a linear inequality.
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