## Math 116: Study Guide - Chapter 5

1. Solve the system of equations by the method of substitution. One linear system, one non-linear system.
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.
3. Solve the system of equations by the method of elimination. Two parts.
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 model and system of linear equations necessary to find the equation of the parabola passing through three points. This is NOT a least squares regression problem. The model is necessary to define a, b, and c in the equations.
6. Solve the system of linear equations. One is a three by three system of linear equations, the other is a two by three system of linear equations.
7. Write an inequality for the shaded region shown in the figure. Two parts.
8. Write the partial fraction decomposition for the rational expression. Two parts.
9. Derive a system of inequalities to describe the region. Two parts. One of the systems is non-linear.
10. Maximize and minimize the objective function subject to the given constraints.
11. Write, but do not solve, the model and system of linear equations necessary to find the equation of a circle passing through three points.
12. Write the three elementary row operations.

### Notes:

• Many of the problems are directly from the text.
• Very few of the problems are exactly the ones that Tami picked (she had a propensity for picking problems I had worked as examples in class - go figure), but most of the problems are very similar, so it should be like the homework.
• Assume all inequalities sketched on the calculator are solid lines.