

1.

Solve the system by the method of substitution.
Check your solution(s) graphically.
a.  (0, 0), (1, –1)  b.  (0, 0), (1, 1)  c.  (0, 0), (–1,
–1)  d.  (0, 1), (0, –1)  e.  (1, 0), (0, –1) 


2.

Use a graphing utility to solve the system of
equations. Find the solution accurate to two decimal places.
a.   b.   c.   d.  no real solution  e.  


3.

Use any method to solve the system.


4.

Solve the system by the method of
elimination.


5.

Solve the system by the method of
elimination.


6.

Solve using any method.


7.

Determine whether the ordered triple is a solution
of the system of equations.


8.

In Super Bowl I, on January 15, 1967, the Green Bay
Packers defeated the Kansas City Chiefs by a score of 15 to 30 . The total points scored came
from 13 different scoring plays, which were a combination of touchdowns, extrapoint kicks, and field
goals, worth 6, 1, and 3 points, respectively. The same number of touchdowns and extrapoint kicks
were scored. There were six times as many touchdowns as field goals. How many touchdowns, extrapoint
kicks, and field goals were scored during the game?
a.  6 touchdowns, 6 extrapoint kicks,1 field
goal  b.  6 touchdowns, 1 extrapoint kick, 1 field
goal  c.  6 touchdowns, 6 extrapoint kicks, 6 field
goal  d.  1 touchdown, 6 extrapoint kicks, 1 field
goal  e.  1 touchdown, 6 extrapoint kicks, 6 field
goal 


9.

Determine which one of the ordered triples below is
a solution of the given system of equations.


10.

Write the form of the partial fraction
decomposition of the rational expression. Do not solve for the constants.


11.

The predicted cost C (in thousands of
dollars) for a company to remove of a chemical from its waste water is
given by the model
.
Write the partial fraction
decomposition for the rational function. Verify your result by using the table feature of a
graphing utility to create a table comparing the original function with the partial
fractions.


12.

Select an inequality for the shaded region shown in
the figure.


13.

Find the consumer surplus and producer
surplus.
Demand
Supply


14.

Use a graphing utility to graph the
inequality.


15.

Sketch the graph and label the vertices of the
solution set of the system of inequalities. Shade the solution set.


16.

Find the minimum value of the objective function
and where they occur, subject to the indicated constraints.
Objective function:
Constraints:
a.  Minimum at  b.  Minimum at  c.  Minimum at  d.  Minimum at  e.  Minimum at 


17.

Find the minimum value of the objective function
and where they occur, subject to the constraints:
Objective function:
Constraints:
a.  Minimum at  b.  Minimum at  c.  Minimum at  d.  Minimum at  e.  Minimum at 


18.

Find the minimum value of the objective function
and where they occur, subject to the constraints:
Objective function:
Constraints:
a.  Minimum at  b.  Minimum at  c.  Minimum at  d.  Minimum at  e.  No minimum 


19.

The linear programming problem has an unusual
characteristic. Select a graph of the solution region for the problem and describe the unusual
characteristic. Find the maximum value of the objective function (if possible) and where they
occur.
Constraints:


20.

Find the minimum and maximum values of the
objective function and where they occur, subject to the indicated constraints.
Objective function:     Constraints:      
