Graphing Equations

A.) 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?

It depends on the type of equation that is being solved in choosing the best method. The pros of using the graphing method include; help to visualize coordinates, good for estimating solution sets, and easy to see multiple solution sets if they exist. The cons to graphing include; lacks accuracy, hard to graph by hand, solution sets are usually estimates, and not a quick way to determine solution sets when it is not integers. The pros of using the substitution method include; easier than graphing for simple equations, accuracy improves, and this method makes solving for two variables manageable. If a system has many equations or variables, the con is this method becomes monotonous. The elimination method pros include; basically the same as elimination but easier to use with larger numbered equations. The con to elimination is that one misstep can lead to a wrong answer and result in a false solution set.

I do prefer the elimination method because I believe it is easier to solve equations for two variables and with larger numbers, decimals, and fractions. Any method is good to use for simple equations while elimination is easier for me to use for the larger equations or one that include fractions.

If I need a rough estimation of an equation, I would graph. If I had an equation that is simple and straightforward, I would use substitution. Otherwise, I would just use elimination.

B.) Sometimes it is very obvious which method is most efficient to solve a system of equations because of the way the problem is set up. To be efficient, under what conditions would you use graphing? Elimination? Substitution? Provide an example of each.

I would use graphing if the coefficients in the give equations are unusual and I only needed to...