That is such supremely bad writing that it can only come from AI being told to spice up the original opening paragraph, and short of the original author being barely literate (and possibly even then), the original text would have been better writing.
The overuse of the $15 synonyms is almost always a bad idea--you want to use them sparingly, where dropping them in for their subtly different meanings enhances the text. But what is extremely sloppy here is that the possibilities of "no solutions, one solution, infinite solutions" is now being described with a different metaphor for solution here. And by the end of the paragraph, I'm not actually sure what point I'm supposed to take away from this text. (As bad as this paragraph is, the next paragraph is actually far worse.)
Mathematics already has a problem for the general audience with a heavy focus on abstraction that can be difficult to intuit on more concrete objects. Adding florid metaphors to spice up your writing makes that problem worse.
The overuse of the $15 synonyms is almost always a bad idea--you want to use them sparingly, where dropping them in for their subtly different meanings enhances the text. But what is extremely sloppy here is that the possibilities of "no solutions, one solution, infinite solutions" is now being described with a different metaphor for solution here. And by the end of the paragraph, I'm not actually sure what point I'm supposed to take away from this text. (As bad as this paragraph is, the next paragraph is actually far worse.)
Mathematics already has a problem for the general audience with a heavy focus on abstraction that can be difficult to intuit on more concrete objects. Adding florid metaphors to spice up your writing makes that problem worse.