The typical system of equations or inequalities problem gives the system and asks for the graph of the solution. This task turns the problem around. It gives a solution set and asks for the system that corresponds to it. The purpose of this task is to give students a chance to go beyond the typical problem and make the connections between points in the coordinate plane and solutions to inequalities and equations. Students have to focus on what the graph is showing. When you are describing a region, why does the inequality have to go one way or another? When you pick a point that clearly lies in a region, what has to be true about its coordinates so that it satisfies the associated system of inequalities?

### General Information

**Subject(s):**Mathematics

**Grade Level(s):**9, 10, 11, 12

**Suggested Technology:**Adobe Acrobat Reader, Microsoft Office

**Freely Available:**Yes

**Keywords:**Solution sets, equations, inequalities, cpalms, icpalms, illustrativemathematics.org, illustrative mathematics, tasks, mathematics, math, resource, free, freely available, problems-based learning, student activities, Florida Standards

**Instructional Component Type(s):**

**Problem-Solving Task**

**Resource Collection:**Illustrative Mathematics