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01.04.2019: One Lesson of Math - Solving Systems of Equations Algebraically, Part 4


Today's soundtrack is Mortiis - Født Til Å Herske, a haunting darkwave album released in 1993. I added it to my music collection approximately a decade after its release, and I still enjoy it today.



I wasn't able to finish all the questions in my assignment yesterday due to my body losing its battle to the bug I've been fighting off all week. Hopefully I'll be able to finish all of the questions today!


I was having a lot of trouble with one quadratic - quadratic equation yesterday; it's the one that I got stuck on. I started it over today, and ended up having to redo it three times before finally getting it correct. The problems that I ran into were improperly simplifying terms and incorrectly switching negatives/positives while multiplying/dividing. Because there are so many steps in these equations, any single mistake can throw the equation way off. It feels like playing whack-a-mole when something isn't right in these equations.


Through a whole bunch of trial and error, I did make a breakthrough: I've figured out that in a linear-quadratic system, the x-intercepts of the combined quadratic equation will equal y when substituted back into the linear equation, but in a quadratic-quadratic system, the x-intercepts of the combined quadratic equation will equal x when substituted back into Quadratic Equation 1.


Finally, a little treat: I made the graph that you see on the left to check the answer to the last question in the assignment. Enjoy!

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