In this lesson, students recall that a system of equations in two variables is a set of equations that represent multiple constraints in the same situation, and that a solution to the system is any pair of values that satisfy all the constraints simultaneously. Students also revisit the idea that the solution, if there is one, can be represented graphically as the intersection of the graphs of the equations.

Students write a system of equations to represent the quantities and constraints in each of several situations, find a solution that meets multiple constraints by graphing, and then interpret the solution in context. In the process, they reason both abstractly and quantitatively (MP2). As they analyze relationships mathematically and reflect on the results, students also engage in aspects of modeling (MP4).

Some students who recall the work on systems of equations from grade 8 may choose to solve the systems algebraically. This is appropriate and welcome, but it is not necessary to introduce the idea to the class here. Students will use algebra to solve systems starting in the next lesson.