## 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 5.1.15-28, 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. 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 5.3.89-92. You do NOT need to solve the system, only set it up.
5. Use back substitution to find the solution to the system of equations. Look at problems 5.3.5-10.
6. Find the equation of a parabola passing through three points. The model y=ax2 + bx + c is given. Write a system of linear equations that can be used to find the equation of the parabola, solve the system of equations, then write the equation of the parabola. Look at problems 5.3.85-88.
7. Sketch the graph of the inequality. Look at problems 5.4.9-20.
8. Solve the system of equations by the method of elimination. Two parts. Look at problems 5.2.11-20.
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.
10. Given a fraction, come up with the partial fraction decomposition for it. The proper form is given to you, write the basic equation, pick convenient values for x, find the constants, and write the partial fraction decomposition. Look at problems 5.3.55-64.
11. Sketch the graph of the system of inequalities. Look at 5.4.39-50.
12. Find a set of inequalities to describe the region. The equations of the curves are given, you'll need to decide which inequality goes with each one. Look at problems 5.4.57-64.
13. Maximize and minimize the objective function subject to the given constraints. Look at problems 5.5.1-12.

### Notes:

• In #1 and #8, 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.
 # 1 2 3 4 5 6 7 8 9 10 11 12 13 Tot Pts 14 6 8 5 4 8 4 14 10 8 5 5 9 100