Name: ________________________ Class: ___________________ Date: __________
ID: A
Systems Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. A rental car agency charges a flat fee of $32.00 plus $3.00 per day to rent a certain car. Another agency
charges a fee of $30.50 plus $3.25 per day to rent the same car.
a. Write a system of equations to represent the cost c for renting a car at each agency for d
days.
b. Using a graphing calculator, find the number of days for which the costs are the same.
Round your answer to the nearest whole day.
a.
b.
ÔÏÔ c
a. ÔÔÌ
ÔÔ c
Ó
b. 11
ÏÔ
Ôc
a. ÌÔ
ÔÔ c
Ó
= 3.00d + 32.00
c.
= 3.25d + 30.50
= 3.00d + 30.50
d.
= 3.25d + 32.00
b. 6
ÔÏÔ c
a. ÔÔÌ
ÔÔ c
Ó
b. 6
ÏÔ
Ôc
a. ÌÔ
ÔÔ c
Ó
= 3.00d + 32.00
= 3.25d + 30.50
= 3.00d + 30.50
= 3.25d + 32.00
b. 11
Solve the system.
____
____
____
____
ÏÔ
Ô −2x − y = −8
2. ÔÌÔ
ÔÔ x − 5y = 15
Ó
a. (–5, 2)
b.
(–2, 5)
c.
(2, –5)
d.
(5, –2)
ÏÔ
Ô −4x + 4y = −8
3. ÔÌÔ
ÔÔ x − 4y = −7
Ó
a. (3, 5)
b.
(5, 3)
c.
(–3, –5)
d.
(–5, –3)
ÏÔ
Ô 5x + 3y = −6
4. ÔÌÔ
ÔÔ 3x − 2y = 4
Ó
a. (0, –2)
b.
(–2, 0)
c.
(–2, 2)
d.
(2, –2)
5. A system of two linear inequalities ____ has a solution.
a. always
b. sometimes
1
c.
never
Name: ________________________
____
ID: A
6. Find the values of x and y that maximize the objective function P = 3x + 2y for the graph. What is the
maximum value?
a.
b.
maximum value at (5, 4); 32
maximum value at (0, 8); 16
c.
d.
maximum value at (9, 0); 27
maximum value at (0, 0); 0
Short Answer
7. Graph the system of constraints. Then find the values of x and y that maximize P = 40x + 30y.
ÏÔ
ÔÔ x ≥ 0
ÔÔ
Ôy ≥ 0
ÌÔÔ
ÔÔ −2x + 2y ≤ 4
ÔÔ
ÔÔ x ≤ 3
Ó
8. Given the system of constraints, name all vertices. Then find the maximum value of the given objective
function.
ÏÔ
ÔÔ x ≥ 0
ÔÔ
Ôy ≥ 0
Ô
ÌÔÔ
ÔÔ 6x − 2y ≤ 12
ÔÔ
ÔÔ 4y ≤ 4x + 8
Ó
Maximum for C = 4x − 3y
2