Systems of equations can be solved by graphing or by using substitution or elimination. What are the pros and cons of each method? Which method do you like best? Why? What circumstances would cause you to use a different method?
Graphing shows intuitively the practical part -- why we are doing what we are
doing. We can see from the graphs of the two lines how the variables grow or
shrink until they come together at their point of intersection, their solution.
The algebraic methods don't show why we're doing what we're doing, and doesn't
lead us to think of increasing or decreasing variables that are the same values
where they intersect.
The down-side of the graphical method is that it is never precise, because we
cannot draw perfectly straight lines. Only if we are use graph paper and thin
pencils and straight edges can we hope to get much accuracy in our answers by
graphing. The algebraic methods, on the other hand, are perfectly accurate.
Substitution is easier when one of the variable in one of the equations has a
coefficient of 1 or -1 and all coefficients are integers.
Elimination is easier when there are no coefficients with 1 or -1.
As far as which one I like best, I always like the one best that's easiest for
the particular system of equations I'm solving.
[BTW, there are other methods for solving them that you haven't studied yet,
Cramer's rule, Gaussian elimination, and the inverse matrix method.]
Edwin
