Hi Mike. I bought your math guide about a month ago, and it’s great! I do have a question about the daily PWN #5. The explanation says that solutions exist in all quadrants except quadrant IV. But how this helps you come up with the conclusion that a>0 and b>0?
Here’s a link to that question.
The conclusion isn’t that a > 0 and b > 0. The conclusion is that IF a > 0, THEN b > 0. That’s a really important difference! Here’s the same graph from the solution to that question, but with a little added detail (in yellow):
The full solution set is that purple-ish region that is the overlap of the blue and the red. The part highlighted in yellow is the only part of the solution set where the x-values are positive. Therefore, you know that if (a, b) is in the solution set and IF a is greater than zero, THEN the value of b MUST also be greater than zero.
Does that help?