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


1.

Solve the system by the method of
substitution.
a.  (4, 3)  b.  (4, –3)  c.  (3,
4)  d.  (–3, 4)  e.  (–4, 3) 


2.

Solve the system by the method of
substitution.
a.  (–4, –23), (5,
–14)  b.  no real
solution  c.  (–4, –25)  d.  (–4, –25), (5, –16)  e.  (–4, 15), (5, 24) 


3.

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


4.

Solve the system by the method of
substitution.
a.  (5, 102), (3, 56), (1, 18)  b.  (5, 102), (–1, –12)  c.  (–3, –34), (1, 18)  d.  (5, 102), (–3, –34), (0, 2)  e.  no real solution 


5.

Find the sales necessary to break even (R
– C = 0) for the cost C of producing x units and the revenue R
obtained by selling x units. (Round to the nearest whole unit.)
a.  782 units or 852 units  b.  no real solution  c.  852
units  d.  782 units  e.  831 units 


6.

Solve the system by the method of
elimination.
a.   b.  (dependent)  c.   d.   e.  inconsistent 


7.

Solve the system by the method of
elimination.


8.

Solve the system by the method of
elimination.


9.

Find the least squares regression line for the points
by solving the system for a and
b.
Points: space
a.  y = –3.47x
–4.21  b.  y =
3.93x –4.21  c.  y =
2.80x –3.20  d.  y =
–2.66x +2.80  e.  y =
–3.20x +2.80 


10.

Solve the system of linear equations.


11.

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


12.

Write the partial fraction decomposition of the
rational expression.


13.

Write the partial fraction decomposition of the
rational expression.


14.

Write the partial fraction decomposition of the
improper rational expression.


15.

Use a graphing utility to graph the inequality.
Shade the region representing the solution.


16.

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


17.

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


18.

Derive a set of inequalities to describe the
region.


19.

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


20.

An investor has $150,000 to invest in two types of
investments. Type A pays 5% annually and type B pays 6% annually. To have a wellbalanced portfolio,
the investor imposes the following conditions. At least onethird of the total portfolio is to be
allocated to type A investments and at least onethird of the portfolio is to be allocated to type B
investments. What is the optimal amount that should be invested in each investment?
a.  $150,000 in type A (5%), $0 in type B
(6%)  b.  $50,000 in type A (5%), $100,000 in type B
(6%)  c.  $100,000 in type A (5%), $50,000 in type B
(6%)  d.  $0 in type A (5%), $150,000 in type B
(6%)  e.  $60,000 in type A (5%), $90,000 in type B
(6%) 
