1) Solve the following system of equations that model supply and demand for a product:
p - q = 0 ( supply equation )
cp - q = -1 ( demand equation )
where p = price and q = quantity
Solve first when c = 0.999 and a second time when c = 1.001. What does the difference in solutions suggest about the importance of having highly accurate coefficients in the system? Remembering that this is a model of supply and demand, are there any solutions that can be tossed out? Why?
2) What is Gauss Elimination? Write a brief summary of what this is. For what type of systems of equations is the Gauss Elimination technique best suited? Why?
3) What computer applications can be used to graph systems of equations? In what circumstances does it make more sense to graph a system than to use the substitution, elimination, or matrix methods?