## 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 odd problems 5.1.11 - 39*.
2. 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 all problems 5.1.41 - 51*.
3. Solve the system of equations by the method of elimination. Three parts. Look at odd problems 5.2.11 - 29*.
4. 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.
5. Write, but do not solve, 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.
6. Use back substitution to find the solution to the system of equations. Look at all problems 5.3.1 - 6*.
7. 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 odd problems 5.3.9 - 25.
8. Write the partial fraction decomposition for the rational expression. Two parts. Look at all problems 5.4.11 - 5.4.26*.
9. 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.
10. Maximize and minimize the objective function subject to the given constraints. Look at all problems 5.6.1 - 5.6.12*.
11. Take a system of rational equations and convert it into a 2x2 system of linear equations by changing the variables. Look at problem 2.4.53 - 70 in terms of how you rewrote the existing equation as a quadratic by changing variables. Then solve the system of equations. There are no problems in chapter 5 like this. This problem is designed to see how well you can apply what you have learned as opposed to reciting what I've given to you.
12. Find the equation of a parabola passing through three points. Look at problems 5.4.39 - 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.

### Notes:

• *'d problems are directly from the text.