High School Math Worksheets: Shading Systems of Inequalities

📚 Topic Summary

A system of inequalities involves two or more inequality equations. The solution to a system of inequalities is the region where the shaded areas of all inequalities overlap. This overlapping region represents all the points that satisfy all inequalities simultaneously. To graph a system of inequalities, graph each inequality separately, shading the region that satisfies each one. The intersection of these shaded regions is the solution to the system.

When shading, remember that a `>` or `<` symbol uses a dashed line, indicating that points on the line are not included in the solution. A `$\geq$` or `$\leq$` symbol uses a solid line, indicating that points on the line are included in the solution.

🧮 Part A: Vocabulary

Match the term with its definition:

1. Term: Inequality
2. Term: System of Inequalities
3. Term: Boundary Line
4. Term: Solution Set
5. Term: Shading

1. Definition: A line that separates the region where the inequality is true from where it is false.
2. Definition: The process of visually representing the region where an inequality is satisfied on a graph.
3. Definition: A mathematical statement that compares two expressions using symbols like <, >, $\leq$, or $\geq$.
4. Definition: A set of two or more inequalities that are considered together.
5. Definition: The set of all points that satisfy all inequalities in a system.

✍️ Part B: Fill in the Blanks

When graphing a system of inequalities, a ______ line is used for inequalities with `>` or `<` symbols, indicating that the points on the line are not part of the ______. A ______ line is used for inequalities with $\geq$ or $\leq$ symbols, indicating that the points on the line are part of the solution. The ______ region is where all inequalities are satisfied.

🤔 Part C: Critical Thinking

Explain in your own words why it's important to use test points when graphing inequalities. Give an example.