If she’s fairly strong at math, throw out whatever prep book she’s using and get the College Panda math book. It’s by far the best. No comparison.
Use Khan academy for “real” questions. Their prep is free and written by the same company that writes the SAT.
Forget everything about the SAT pre-2016. It was substantially redesigned.
And yes, SAT now loves questions that are fiendish to solve but easy if you understand the concept. For example, on the 2019 PSAT there was a question that gave 2 equations and told the students to solve for C. However, it included the information that the lines were parallel, and if you looked at the equations, C was the slope in one. You could literally see the answer.
I teach GOOD math students. The vast majority tried to grind out that answer.
Sure, you can set up the obvious 2 by 3 matrix and row reduce it. This is just Gaussian elimination in a slightly easier format and I what I would use. Except for Cramer’s rule, all methods are just notational variants. Cramer’s rule has some theoretical uses, but is useless as a practical matter.
The reason I preferred elimination to substitution for the problem in question is that operations on the entire row seem to be less prone to errors. The removal of denominators and changes in sign for the entire row are done at the same time.
To quote one of my sister’s profs, “I’m only teaching you Cramer’s rule because you might run into some crusty old engineer who’ll say, ‘They never taught you Cramer’s rule?! What’s the point of your big fancy schooling then?’”
That being said, I did encounter one problem where Cramer’s rule was used and other techniques couldn’t. It was a differential equations proof that resulted in a system of linear equations that needed to be solved, and Cramer’s rule allowed you to write down the solutions in closed from (in terms of some determinants) and use those solutions in the proof.
Not quite sure what the point is of your condescending snark; yes I am well aware of the fuzzy nature of the line in question. Quite often my students will know how to solve or simplify things, by rote habit, but will be utterly unable to apply them to concrete situations (which is now a big part of the test), or think outside the box when a different more novel approach would be much more efficient and less error-prone.
Most of what gets taught as “using matrices to solve a system of equations” is just “do the same steps you would have done anyway, but don’t write down the letters for the variables”. It’s a little more concise, but it’s also harder to follow conceptually, and I think that, for most students, that’s a poor trade.
The one place where matrices are really useful for solving systems is when you have a whole bunch of problems, related in such a way that you can solve all of them by using the inverse of the same matrix.
Matrices are also quite useful for transformations, and in particular compositions of transformations (in fact, I would say that this is the primary use for matrices). But for some reason, this is never covered in high school classes.