Just to clarify.. is she is a CC compressed Math 8, Algebra I class combined? If so.. Math 8 isn't "pre-algebra" it is pre-algebra the first 4-5 chapters of Algebra & some gemoetry.
Techncally, she is in prealgebra. (How systems of equations is prealgebra, I don't know.) Next year, she will take Algebra 1. I'm still confused about how this all works.
In the decent schools with which I am familiar, Pre-Algebra is not your parents' Pre-algebra. Perhaps partly because of all the exposures to "elementary algebra" and "elementary geometry" in the standard elementary curriculum, Pre-algebra is half review of elementary math and half beginning Algebra and beginning Geometry. In her GT Algebra I course, DD12 (7th) finished systems of linear equations and systems of linear inequalities a couple of months ago.
Systems of linear equations may be a bit early for Pre-Algebra and DD's GT Pre-Algebra course (using a standard textbook) did not cover it last year. However, three years ago, DS12 used a pre-2000 Pre-Algebra book in his extra-accelerated program that was specifically marketed for GT only and did cover systems of equations during the second half of the year.
Anyhow, here are my advice as related to your original concern although I must confess that I haven't dealt with brick walls or re-teaching as some PP have. First, I cannot overemphasize how critically important it is for your DD to graph graph graph graph graph. It is the key to conceptual understanding. Ultimately, she needs to look at an equation or an inequality (rather it is linear or non-linear) or a system of equations/inequalities and visualize what it looks like and therefore what it means. In fact, I think this is in part why the current curriculum order looks so jumbled and spirally to many - the objective is to provide a big picture structure/frame to be filled in rather than a linear approach of one subject followed by another and within each subject brick by brick.
Another advice is to put the system of equations in context - this is a standard requirement in our district even pre CC when my oldest took Algebra I 5 years ago. Make sure she can set up two linear equations based on a real life problem or in the beginning at least understand what two linear equations can represent in real life. For example, constraints on spending/purchases are relevant to a tween/teen. You don't want your DD to mechanically follow a procedure to solve for X and Y. You want her to see why she would bother.
Finally, use AOPS alcumus to check her foundation in Pre-Algebra. If she has mastered Pre-algebra, it doesn't take very long to pass all the Pre-algebra topics plus in the process she wil deepen her understanding. DD12 who is strong in math but not mathy by inclination/thinking breezed through school Pre-Algebra last year but I was concerned with the adequacy of her school curriculum so I had her go through alcumus Pre-Algebra. She passed all the alcumus Pre-algebra topics pretty quickly during the summer but did learn some new stuff/approaches, which I think probably contributed to her finding Algebra I really easy this year. Anyhow, my point is that a solid foundation in Pre-Algebra is critical before you can build the structure of Algebra, Geometry, Trigonometry on top.
