Expert: Scott A Wilson - 7/13/2010

Question
Hi, I am really having a hard time in my algebra class- I have tried to read the text but it might as well be in a different language. I have two questions for you:
1.Systems of equations can be solved by graphing, using substitution, or elimination.
What are the pros and cons of each method?
What circumstances would cause you to use a different method?
(I dont even know what elimination is??!)
Thankyou in advance :)
Noelle

Answer
Graphing lets the solution be visualized and has the fewest errors.
The problem is it can be done with only two variables (or maybe 3, if good at 3D drawing.

Substitution is where a varible is solved for and put into the other equation(s).
This eliminates one variable at a time and is fairly easy to follow.

Elimination is the best way for more than two variables, but does the most things at once.
It is generally used in matrix format with several rows and columns.  The constants in each column are for each variable.  Like the first column of constants would be for x, the second column of constants for y, etc.  This method divides an entire row by the value in one cell, and then subtracts the right multipliers by that row from the rest of the rows to make them all 0.

Depending on how many variables there are, I use substitution or elimination.
Two variables lead to substitution and four or more is elimination.
Three variable is a toss up between the two depending on how it looks.
If there are only two variables and graphing is fairly easy, sometimes I use that to get a picture of how it looks.