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?

Thank you!

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?