2.14.7 Lesson Summary

In this lesson, you learned how to:

• Write a system of inequalities to describe a situation, find the solution by graphing, and interpret points in the solution.
• Explain what is meant by “the solutions to a system of inequalities” and describe the graphs that represent the solutions.
• Find values that satisfy each constraint individually, and values that satisfy both constraints at once, when given descriptions and graphs that represent two different constraints.

Here are the activities that helped you reach those goals:

• 2.14.1: Modeling Equations to Solve a Riddle
  • In this activity, you reviewed systems of equations and their solutions. You recalled that a solution to a linear equation in two variables is any pair of numbers that makes the equation true, and that a solution to a system of two equations in two variables is a pair of numbers that makes both equations true.
• 2.14.2: Finding a Pair of Values that Satisfy Multiple Inequalities
  • In this activity, you encountered a situation in which two constraints can be expressed with inequalities represented on two separate graphs, which made it challenging to find pairs of values that meet both constraints simultaneously. This served to motivate a desire to represent both constraints on the same graph.
  • 2.14.2: Self Check
  • 2.14.2: Additional Resources
• 2.14.3: Writing Systems of Inequalities that Represent Situations
  • In this activity, you wrote systems of inequalities that represent situations and found the solutions by graphing. Your focus was on thinking about each pair of constraints as a system, finding the solution region of each inequality, and identifying a point in the region where the graphs overlap as a solution to the system.
  • 2.14.3: Self Check
  • 2.14.3: Additional Resources
• 2.14.4: Graphing Solutions of Systems of Inequalities
  • In this activity, you reviewed the idea that the solutions to a system of inequalities can be effectively represented by a region on the graphs of the inequalities in the system. You began to graph systems of inequalities.
• 2.14.5: Writing Inequalities for Situations and Representing on a Graph
  • In this activity, you wrote an inequality for given statements and identified graphs that represented each inequality.

After these activities, you completed the following practice:

• 2.14.6: Practice