## Math 116: Study Guide - Chapter 5

1. Solve the system of equations by the method of substitution. One linear system, one non-linear system. Look at problems 5.1.11 - 39.
2. Find the system of linear equations which has the given solution. There is more than one possible solution. One part has an ordered pair, the other part has an ordered triplet.
3. Use a graphing calculator to approximate all points of intersection of the graph of the system of equations. One system involving transcendental functions, one non-linear system. Look at problems 5.1.41 - 51.
4. Write the system of linear equations necessary to find the equation of a circle passing through three points. The model is given to you. Look at problems 5.3.43 - 46. You may use Derive to solve the system of equations.
5. Use back substitution to find the solution to the system of equations. Look at problems 5.3.1 - 6.
6. Find the equation of a parabola passing through three points. Look at problems 5.3.39 - 42. You will need to give the generic model (y=ax2 + bx + c), substitute in the values for x and y, solve the system of equations, and then write the final model. You may use Derive to solve the system of equations.
7. Solve the system of equations by the method of elimination. Two parts. Look at problems 5.2.11 - 29.
8. Solve the system of linear equations. Show your work. One is a three by three system of linear equations, the other is a two by three system of linear equations. Look at problems 5.3.9 - 25.
9. Write the partial fraction decomposition for the rational expression. Look at problems 5.4.11 - 5.4.27.
10. Derive a system of inequalities to describe the region. Two parts. One of the systems is non-linear. Look at problems 5.5.51 - 60. The equations are given, all you have to do is put in the correct inequality.
11. Maximize and minimize the objective function subject to the given constraints. Look at all problems 5.6.1 - 5.6.12.
12. True or False.
1. Know what consistent / inconsistent systems are.
2. Know when a unique solution is possible and when it isn't.
3. Know how to write a dependent solution
4. Know the fundamental theorem of linear programming
5. Know when a maximum and minimum will occur in a linear programming problem.

### Notes:

• None of the problems are directly from the text.
• Show work on all problems except where otherwise indicated.
• You may use Derive to check your answers, but you still need to show work.
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