In proving that the elimination method of adding linear equations works, does one need to show that it is equivalent to substitution?
Using the transitive or substitution property to solve a system of equations is on solid ground because those can be taken as postulates. However there is no elimination postulate, is there?
Also if you don't write y=x+4 and y=2x like so but instead as
f(x)=x+4 and g(x)=2x
then if you add and get
and then write it as
then we are implicitly setting f(x)=g(x) right? I guess by using the same letter, y, for each line is just a shortcut for not having to explain what is really going on. Prof. Jerison mentions this "sloppiness" in the first lecture of MIT's OCW Calculus.