My only suggestion for understanding two equations & two unknowns then uses graphs? Solve with graphs first. Graph the equations & see where they overlap. IMO this is one of the best ways of understanding what is going on. Graph lots & lots of different equations. Graph them on top of each other and see where they intersect. Graph the different steps, so you can see that equations that look different are really equal.
I'd agree. This is, btw, the approach taken by the secondary math stream of the Singapore Math series I've used with some of my children (Discovering Math/Dimensions Math CC; I prefer the sequence of Discovering over Dimensions). Plenty of graphing prior to introducing substitution or elimination, so that students understand that the solution of simultaneous equations is the coordinates of the point of intersection between lines, not just some procedural manipulation. Find a free equation graphing app (our iMac appears to have come with one) and graph them that way, if hand-drawing them becomes overly laborious.
