Yes, both equations will always work, but yes, at times it is more logical to use one over the other. for instance:
x-4y=6
x+4y=12
we see here that elimination would best fit:
x+x+4y-4y=6+12
or:
x=2y-3
7x+3y-81=23
substitute (2y-3) for x.
Also, once you have a single placeholder, put it ito quadratic form (ax^2+bx+c=0)
and use the quadratic formula:
x=(-b±sqrt(b^2-4ac))/2a
