If you have students write, they will make great connections. I find this student's writing particularly clear and it is obvious to me that he "gets" the bigger picture of different ways to solve systems of equations:
I learned a lot in Chapter 6. We learned about all the different ways of solving a system of equations. We reviewed the equal values method, where you make each equation equal to the same thing, make them equal, and then solve for the variables. We learned about the substitution method, where, for instance, if you had one equation in a y=mx+b form, you replace y in the other equation with whatever mx+b is. Then, finally, we learned about the elimination method, where you try to get rid of one of the variables. For instance, if you have two equations: x+2y=1, and 3x+5y=8, you would want to multiply the first equation by 3 so you would have 2 "3x's" and then subtract the second equation from the first equation. This method is very useful because it is quick and easy. I think my favorite method is the substitution method. The substitution method can almost always be used and it is also very easy and pretty simple. I don't like he equal values method because it takes a really long time for me and it seems a little more complicated than the others. The elimination method isn't bad, it works pretty well but it is less useful than the substitution method in my opinion.