For use after Lesson 5.7 In your own words, write the meaning of each vocabulary term. system of linear inequalities solution of a system of linear inequalities graph of a system of linear inequalities

Certainly! Here are the meanings of each vocabulary term explained in your own words: 1. **System of Linear Inequalities** - A **system of linear inequalities** consists of two or more linear inequality statements that are considered together. Each inequality defines a region on a graph, and the system seeks to find all the points that satisfy **all** the inequalities at the same time. For example, you might have two inequalities like \( y > 2x + 1 \) and \( y \leq -x + 4 \), and the system would include all the points that make both of these statements true simultaneously. 2. **Solution of a System of Linear Inequalities** - The **solution of a system of linear inequalities** is the set of all possible points (usually represented as (x, y) coordinates) that make every inequality in the system true at the same time. This means finding where all the shaded regions from each inequality overlap on a graph. Any point within this overlapping area is a solution because it satisfies each inequality in the system. 3. **Graph of a System of Linear Inequalities** - The **graph of a system of linear inequalities** is a visual representation on a coordinate plane that shows all the possible solutions to the system. Each inequality in the system is graphed as a line (solid or dashed, depending on whether the inequality is inclusive or not) along with a shaded region that represents all the points that satisfy that particular inequality. The area where all the shaded regions from the different inequalities overlap is the graph of the entire system, highlighting where all the inequalities are true together.