This problem indeed appears more advanced than typical Algebra 1 material. While basic matrix concepts might be introduced in Algebra 2 and further explored in precalculus, the specific methods used here, such as Gaussian elimination and partial pivoting, are generally taught in college-level linear algebra courses.
It's less common, but possible, for these topics to be touched upon in AP Calculus or AP Statistics. If you're currently in an Algebra 1 course and encountering this problem, it might be worthwhile to discuss with your instructor whether this is the expected level of complexity for your assignments.
In case you are enrolled in a higher-level course, aligning this question with that subject area could yield more relevant assistance and insights.