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Question 1103650: I teach Algebra 2. We are solving systems of inequalities by graphing. I was intrigued to notice that there appeared to be a "hole" in the answer key graph where one inequality (inclusive) intersected with another inequality (not inclusive) - e.g. where an equation with "less than or equal to" intersected with one that was "less than." I had never noticed "holes" in graphing solutions of inequalities before. This brought up the question: is the point of intersection of the two linear graphs - one dashed and the other solid - included in the solution or not? When we solve the system, I understand that we are looking for the "intersection" rather than the "union" of the system. That suggests that any solution point must satisfy all constraints at once. The point of intersection of the two lines would satisfy only one of the two inequalities, since one of the lines is not inclusive. So, should we teach students to insert a "hole" at that point of intersection?
Answer by ikleyn(52794)   (Show Source):
You can put this solution on YOUR website! .
The best step from your side would be posting a concrete example.
I mean - a concrete system of inequalities.
Or two or three, if you need.
Start posting ONE system.
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