Students are prompted to graph f1(x) = -9 + 2x and f2(x) = -9 + 2x and estimate the coordinates of their intersection. They then Trace the graph of f1 and see that the intersection point is approximately (8, 7). Next they trace f2 and see that the point (8, 7) also lies on its graph. Then they trace both functions at once as see that as the identical x-values of the two points approach 8, their y-values get closer to each other.

Next, students add a function table to their graph and examine it in search of an x-value that gives the same y-value for both functions. This point, (8, 7) is defined as the solution to this system of linear equations.

Note: when students add a function table to their graph, students will not be able to see all 3 columns because of the size of the window. The .tns file directs them to switch the page layout from a vertical to a horizontal split. Alternatively, students can open the Tools menu (/ + b) and choose Page Layout > Custom Split. This allows them to adjust the panes of the window with the arrow keys. Pressing enter sets the panes and returns them to the activity.

In Problem 2, students are directed to try another system, f1(x) = 7 + 3/2(x) and f2(x) = 35.9 - 6x. This time, students must adjust the table settings in order to find the x-value that gives the same y-value for both functions.

Students should try other systems, like f1(x) = 2x + 7 and f2(x) = -3 + 2x, as well as systems that include nonlinear functions.