📚 Topic Summary
Graphing systems of linear inequalities involves graphing two or more inequalities on the same coordinate plane. The solution to the system is the region where all the inequalities overlap, representing all the points that satisfy every inequality simultaneously. The boundary lines are dashed for strict inequalities ($<$ or $>$) and solid for inclusive inequalities ($\leq$ or $\geq$). This overlapping region is often shaded to clearly indicate the solution set.
🔤 Part A: Vocabulary
Match the term with its definition:
| Term |
Definition |
| 1. Inequality |
a. A line on a graph that shows the boundary of an inequality. |
| 2. System of Inequalities |
b. A mathematical statement that compares two expressions using symbols like $<$, $>$, $\leq$, or $\geq$. |
| 3. Solution Set |
c. Two or more inequalities considered together. |
| 4. Boundary Line |
d. The area on a graph that satisfies all inequalities in a system. |
| 5. Half-Plane |
e. The region on one side of a line, extending to infinity. |
✍️ Part B: Fill in the Blanks
Complete the following paragraph using the words: dashed, solid, overlapping, inequalities, solution.
When graphing a system of _____, we are looking for the region where all the _____ regions intersect. This _____ region represents the _____ set. Boundary lines are _____ if the inequality is strict ($<$ or $>$) and _____ if the inequality includes equality ($\leq$ or $\geq$).
🤔 Part C: Critical Thinking
Explain, in your own words, how changing the inequality sign (e.g., from $<$ to $\geq$) affects the graph of the solution set in a system of linear inequalities. Give an example.