Exploring Linear Inequalities

Hidden Treasure

Consider the graph of the following system of inequalities: The first inequality is y is less than or equal to x plus 1. The second inequality is y is greater than or equal to negative x plus 1. When graphed, the system includes two solid lines that form an x-shape, intersecting at (0, 1). Imagine that the upper region created by the x is shaded one color, that the lower region created by the x is shaded another color, and that the region created to the right of the x is shaded some third color that is a combination of the first two colors, indicating that it is where the other two regions overlap.

Select one of the ordered pairs from the overlapping shaded region described above. There may be more than one point that falls in the overlapping shaded region, but you’ll have to try your luck and pick just one to play. Select Check Your Work to see if you are correct. Good luck!

1. (1, 3)
2. (5, negative 3)
3. (8, 4)
4. (negative 2, 6)
5. (6, negative 2)