Drag the locators to move the lines. Each locator snaps to the
nearest point with integer coordinates. The equations of the
lines are displayed on the right as a two-by-two system of
linear equations with integer coefficients. Provided that a
unique solution exists, it will be displayed as well (the
solution is the point of intersection of the two lines). It is
not hard to position the lines in such a way that the solution
will also be a point with integer coordinates. This
Demonstration can be used to generate thousands of such
examples. Mathematics instructors can use it as a simple tool
for creating problems for beginning students. You can also use
it to challenge more advanced students; for example, among all
systems that can be generated here whose solution has integer
coordinates, can you find one whose solution is farthest from
the origin?