Students are prompted to graph three different linear systems on three different screens and state how many solutions each have. This introduces all the possible numbers of solutions and connects them to the graphs of the systems. Help students connect what they see in the graphs with their experiences solving systems by asking them to find the points that represent solutions and write their coordinates.

In this problem, students are given a line and challenged to draw additional lines to form linear systems with particular numbers of solutions. They then use the Coordinates and Equations tool to find the equation of the lines they drew. These equations are recorded in a table on their worksheet. This data is used to answer a series of questions, guiding the student to state rules that for the number of solutions of a linear system can be determined by the coefficients of the equations. Finally, these rules are applied to determine the number of solutions of a system without graphing.