Comments by "SmallSpoonBrigade" (@SmallSpoonBrigade) on "Can you solve this equation?" video.

Yep, those are also good ways to go about it.
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@Douglas_Blake That's due to bad instructional practices. When I was a kid learning arithmetic in the '80s we weren't even allowed to have a calculator until we could do a bunch of this stuff by hand. In recent years it's become trendy to focus on the concepts and neglect the ability to do this stuff by hand. I once worked with a student in calculus III that couldn't function without a calculator to do the arithmetic. Calculators are helpful, but it can take a long time to mess around with the calculator if you have to do that even for basic multiplication and division that's included in the 12x12 times tables. And, it takes less than 3 months to learn all of them just learning one a day.
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@jstnxprsn No, back then they just didn't have the option of permitting calculators to do a bunch of this for the students. So, the stuff the students could do had to be done by hand, and it makes it a lot harder to get correct answers without learning anything when it's being done by hand rather than calculator. The math being done now is in a lot of ways better than what was being done back then, because they do have the option of using calculators to speed up long calculations. And graphic calculators to see what things look like almost immediately so they can go through the cycle of prediction and verification so much faster. Chances are that back in the '70s you wouldn't really ever consider what this stuff looked like unless it was relatively simple.
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Yes, or it's a broken problem, but either way it's worth taking a bit to consider what's going on because that's not an acceptable result. In general when you have a step where all the variables disappear, you have to take a step back and consider what's happening. Often it's a mistake, sometimes it's the result of there just not being a solution, for example, looking for where Y=5x crosses Y = 5x +1. They're parallel, and won't cross without freaky curved surfaces. Or, if we're in 3, or more, dimensions, they could be skewed.
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Infinity usually doesn't count here because it's a concept and not a number. There may be situations where that's an acceptable answer to this, but we're normally not looking for trivial answers and infinity when we're solving things like this.
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@DJF1947 It can be, but usually it's not.
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