# Solving systems Essay

## Solving systems

Solving systems of equations can be applied to many situations. For example, systems of equations can be used to find the optimal number of items to produce to ensure the highest profitability of those particular items. Systems of equations can be solved by four methods: graphing, substitution, elimination, or with matrices. Which method do you prefer when solving a system of equations? Why? What circumstances would cause you to use a different method?

Personally, the method a use for any particular set of equations depends largely on the dimension of the set of equations. That is, my choice depends on how many unknown variables there are and how many equations are in the set; which would translate to how many columns and how many rows, respectively, when in matrix notation. When the number of equations is only about two or three, I prefer to use elimination. Elimination works best for these as it is very fast, because once you pair off equations that look similar you can find a variable you can isolate immediately.

For more than three equations however, elimination does not work so very well; I tend to go around in circles and retrace my steps and try different approaches, and sometimes I even switch to substitution after I reach a dead end. For more or less the same reasons, I use elimination for when there are only two or three unknown variables because you only need a few steps to isolate each one, and most times you do not need to use all the given equations. For sets of equations with more than three equations and/or unknown variables though, I prefer to solve these using matrices.

Solving a set of equations with several variables and equations can be very simple when you convert them to matrix form and use row reduction. It takes a little long sometimes but it never gets confusing, all you need is to do is systematically work on column after column and by the time you reach the end you can always be sure that you have your solution set. PAGE TWO Deliverable Length: 250 words minimum, Details: The use of sets is important in many areas, such as market research, politics, and medicine.

For example, a college student may be in a particular set depending on a degree program: Degree = {Associate, Bachelor, Master, Ph. D. }. A second related set might be a listing of majors: Major = {Accounting, English, History, Math, Psychology,… }. Set operations can also be performed on these sets. For example, the union of the sets would be a listing of all degrees and majors; an intersection might be an Accounting PhD student; the complement would be a member not in the set. The complement of the major set could be a Geology major.

Provide a real-world example that shows 2 related sets. List all the members of your sets in set notation. A set can consist of individuals, objects, etc. Then, for that example show the union and intersection for those two sets. Show the complement of both individual sets. I actually stumbled across an article just lately that was about a case study of first responders, firefighters specifically, who helped at the World Trade Center after the attack, shortly after and during the collapse.

The study was a biomonitoring (testing of the internal dose of chemicals or a metabolite ion body matrices, which include blood and urine) of the subjects to see how much harmful chemicals were in their bodies due to all the combustion products from the initial collapse and the fires that kept going for months on after. The study tried to characterize the amount of chemical dosage according to certain parameters such as normal demographics (age, gender) and, more importantly, assigned tasks and arrival time.

The assigned tasks were to see whether what the firefighters were doing affected the internal doses, and this can be listed as the set: {rescue, squad, marine units, ladder, engine, hose}. Each firefighter’s arrival time, measured relative to the actual collapse, was noted to see if the exposure to combustion particles got worse or better in the next couple of days and these can be represented by the set: {present at WTC collapse, arrival on days 1 or 2 postcollapse, arrival on days 3-7…}.

The elements of this set go on until the time of the sampling, which was 3 weeks later. The union of these sets would be the set of all firefighters who responded to the scene of the WTC collapse. An intersection would be a firefighter who worked the hose on the day of the collapse. A complement of the assigned tasks set would be a firefighter who arrived at the scene but maybe got injured and had to leave without completing a task, and a complement of the arrival time set would be a firefighter who, for one reason or another, never got to arrive on the scene.