# Math 116 - Chapter 5 Study Guide

1. Solve the system of equations by the method of substitution. One linear system, one non-linear system. Look at problems 5.1.15-28, 41-42, 49-50.
2. Find the system of linear equations that has the given solution. There is more than one possible solution. One part has an ordered pair, the other part has an ordered triplet. Look at problems 5.2.57-60, 5.3.41-44.
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 5.1.37-50.
4. Use back substitution to find the solution to the system of equations. Look at problems 5.3.5-10.
5. Sketch the graph of the inequality. Look at problems 5.4.9-20.
6. Sketch the graph of the solution of the system of inequalities. Look at problems 5.4.39-50.
7. Solve the system of equations by the method of elimination. Two parts. Look at problems 5.2.11-20.
8. Find the partial fraction decomposition for a rational expression. Write the basic equation, pick nice values for x and find the constants. Finally write the partial fraction decomposition. Look at problems 5.3.55-64. This is a nice problem in that the factors are all linear and not repeated. There is another problem on your take home exam that is more involved.
9. 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 5.3.13-21, 33-38.

## Notes:

• In #1 and #7, you are instructed to use a specific method to solve the system of equations. If you are unable to use that method, go ahead and use a different method to solve it and get some partial credit for the problem.
• Show work on all problems except where otherwise indicated.
• There is a take home exam for this chapter worth 30 points. It is due the day of the exam.
• There are not many problems on the in-class test, so each one is worth a lot of points. Make sure you know the material well.

## Point values for each question

 # Pts 1 2 3 4 5 6 7 8 9 Total 12 6 8 4 4 6 12 8 10 70