Name:    Chapter 8 Pre Test

Multiple Choice
Identify the choice that best completes the statement or answers the question.

1.

Select the graphs of the equations and approximate any solutions of the system of linear equations.
 a. d. infinitely many solutions b. e. no solution c.

2.

Find the system of linear equations below that has the solution

, , , ,
 a. b. c. d. e.

3.

A small company produces bird feeders that sell for per unit. The cost of producing each unit is , and the company has fixed costs of . Let the cost function be the total cost to produce x bird feeders and let the revenue function be the total revenue from selling x bird feeders. Graph the cost and revenue function and find the point of intersection of the graphs.
 a. d. b. e. c.

4.

If possible, solve the system below by the method of elimination. Use the graph to check the solution.

 a. b. c. d. e.

5.

If possible, solve the system below by the method of elimination.

 a. b. c. d. e.

6.

You invest a total of in two investments earning and simple interest. (There is more risk in the fund.) Your goal is to have a total annual interest income of  . The system of equations that represents this situation is

where x represents the amount invested in the fund and y represents the amount invested in the fund. Solve this system to determine the smallest amount that you can invest at in order to meet your objective.
 a. b. c. d. e.

7.

Solve the system of linear equations below.

 a. b. c. d. e.

8.

Solve the system of linear equations below.

 a. b. c. d. e.

9.

Solve the system of linear equations below.

 a. b. c. d. e.

10.

Find the position equation for an object that has distance at second, at seconds, and at seconds.
 a. b. c. d. e.

11.

The sum of the measures of two angles of a triangle is the measure of the third angle. The measure of the second angle is than the measure of the third angle. Find the measures of the three angles.
 a. The first angle is , the second angle is , and the third angle is . b. The first angle is , the second angle is , and the third angle is . c. The first angle is , the second angle is , and the third angle is . d. The first angle is , the second angle is , and the third angle is . e. The first angle is , the second angle is , and the third angle is .

12.

Write the system of linear equations represented by the augmented matrix below. Use variables x, y, z, v, and w.

 a. b. c. d. e.

13.

Describe the elementary row operation used to transform the first matrix

into the second matrix .
 a. Add times the third row to the second row. b. Add times the second row to the third row. c. Add times the third row to the second row. d. Add times the second row to the third row. e. Add times the second row to the third row.

14.

Solve for in the matrix below by using elementary row operations to form a row-equivalent matrix.

 a. b. c. d. e.

15.

Find the determinant of the matrix below.

 a. b. c. d. e.

16.

Determine whether the points ,, and are collinear.
 a. The points are not collinear. b. The points are collinear.

17.

Use a determinant to find the equation of the line through the points and .
 a. b. c. d. e.

18.

Determine if the ordered pair is a solution of the system of linear inequalities .
 a. not a solution b. solution

19.

Graph the system of linear inequalities below.

 a. d. b. e. c.

20.

Graph the system of linear inequalities below.

 a. d. b. e. c.