This is three different versions of the same activity. Students are shown a system of inequalities and the graph it produces on a coordinate grid. There are 10 different points placed onto the graph and students are asked to sort the 10 points on a T chart into either answers or not answers. After they sort them on the T chart the students are asked to provide justifications for some of their beliefs.
I have included three different versions of the activity as well as answer examples for all three pages. I initially tried to create the shading on the coordinate grids in color as well as patterns, but the colors did not look nearly as nice as the patterns. With the colors, there ended up being three different colors on the grid while with the use of patterns students are more clearly able to see the intersection of the two shaded areas. One inequality uses small + signs as shading and the other inequality uses small O’s. Where the two intersect you can see both +’s and o’s. It made the intersection of the shaded areas of the inequalities much more noticeable for the students.