I'm going to disagree and agree at the same time. Yes, in the current situation, graphing the lines will help. But IMO, it doesn't address the fundamental problem, which is that current teaching doesn't create a proper foundation.
Here's how the ancient pre-algebra book handles the idea of functions in chapter 1 (set theory):
Section 1.3 focuses on 1:1 correspondence between sets. Section 1.4 introduces a function in terms of 1:1 pairs between sets. It uses diagrams of sets to depict definitions for domain and range. Then it gets into the idea of one input ---> one output = function. It next brings up the subject in the final chapter (intro to functions and basic graphing).
Knowing this stuff is essential to getting what it means to solve a pair of equations. The intersecting graphs help IF the student has a solid understanding of function and intersecting sets, which I suspect is extremely unlikely in pre- or early algebra, especially as taught today.
I could be wrong; the OP could ask her daughter to explain functions and see what she says. She could also ask how the intersecting lines relate to set theory. If the answer is something like, "the point where the lines meet is the intersection of the sets of the two ranges," she understands. I suspect that very few kids get this. Yet it is so fundamental....
