You can find the information you desire more quickly, if you use appropriate key words to do your own search. Also see http://hanlib.sou.edu/searchtools/.
For "math substitution method," I found:
Do the same for the elimination method and make your comparison.
it all depends upon the equations in question:
if equations are VERY straight forward then the graphing method can work
well. It has the advantage of visualation. In other words, you can see the behaviour of the system. Main drawback to graphing is it isnt very accurate for
For other short and simple equations substitution can work well. The advantage to substitution is when one of the variables is already isolated in one of the equations. Even then you must look closely at the other equation to see how complicated the substitution method could be. A few drawbacks to substitution is there can be alot of division and finding LCM.
I would say the elimination method is the most popular and in my opinion is the best .Many times you can even do calculations in your mind, and so it is much faster. Elimination seems to be more useful when coefficients are larger, whereas substitution is useful when coefficients are smaller and when it is easy to islate a variable. Elimination works for any system of linear equations. After one or two steps you have a one-step equation to solve and you have half of your solution. Con can be Sloppy calculations can lead to incorrect solutions
If I need a rough idea of the solution, I graph. If one of the equations is already solved for y or for x, I use substitution. If neither of the above is true, I use elimination.