2. College algebra concludes at the point where we learn how to solve systems of

Question

2. College algebra concludes at the point where we learn how to solve systems of linear equations in three variables through substitution and elimination. However, this is only the beginning of how algebra can be applied to real life problems. At the heart of every application of systems of linear equations, non-linear equations or even inequalities, is a set of constraints: finite amounts of resources, time, physical limitations, etc.

a. Choose an industry that you think might use such systems and discuss the constraints they might encounter.

b. How do they quantify them?

c. Are there alternate methods, materials, or sources at their disposal?

Explanation / Answer

Automobile industry uses these kind of systems. They have to solve so many system of linear equations to solve for the best design of car body or engine parts or other similar things.

There are equations with so many variables that can't be relied to be solved through elimination and substitution. It can take so much time.

Quantification of physical variable are done using laws of physics. Using Newton's laws, drag force equations, force balance etc.

Now, there are softwares to solve those equations using better numerical techniques like gauss elimination and back substitution.

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