Unit 3 Exam REVIEW
1. Which of the following systems has the
solution (-19, -14)?
A 3x – 2y = –1
C 4x + y = 7
6x – 4y = 6
B –3x + 4y = 1
2x – 3y = 4
x + 4y = 4
D 3x – 4y = 2
–2x + 4y = 9
2. What are the vertices of the feasible region
bounded by the constraints?
𝒙≥𝟎
𝒚≥𝟎
𝒚 ≤ −𝟐𝒙 + 𝟖
3. An astronomer has developed the
following system of equations based on
the paths of two asteroids in the same
plane. At which coordinates do their
paths intersect? Solve using elimination.
4x – 2y = 8
x + 2y = –3
4. Your friend wants to solve the system
using elimination.
 3x – 4 y = 1

5 x + 2 y = 7
Which is the best way for your friend to
proceed?
5. Which is the solution to the system?
 6x + 5y + 2z = 41

 4x – 10z = – 10
 – x – 2y + 2z = – 1

6.
A student has 10 coins in her pocket
that have a value of $0.85. The coins are
either nickels or dimes. Which system
of linear equations represents this
scenario?
F
Give a solution and a non- solution to
the system of linear inequalities.
7.
y  x – 3

x + y  2
8.
Which system of linear equations does
the graph show?
 x  y = 0.85

0.5x + 0.10y = 10
 x  y = 10

0.5x + 0.10y = 0.85
 x  y = 0.10
H 
5x + 10y = 0.85
G
J
 x  y = 0.85

5x + 10y = 10
 y =  2x + 1

 y =  3x  4
 y = 2x + 1
B 
 y =  3x  4
A
 y =  2x  1

 y =  3x  4
 y = 2x  1
D 
 y =  3x  4
C
9.
Graph the system and give the solution.
 x – 3y = – 6

x + y = – 2
11. What is the x-value in the solution to the
system of linear equations?
y  1 x  2

2

y – 3 x – 2
2

12. What is the x-value of the solution?
4x – 2y + 4z = –16
x + 2y – 3z = 9
3x – y – 4z = 3
10. A classmate graphed the system of linear
equalities incorrectly, as shown. Which
best describes his mistake?
 x – y  –2

 x + y  –1
F The line that represents x – y ≥ –2
should be dotted.
G He graphed the line x – y = –2
incorrectly.
H He shaded the incorrect half plane for
x + y > –1.
J The region that represents the
solution should be bounded by
4 sides.
13. List three methods used to solve systems
of equations. Describe the strengths of
each
method.
14. Graph.
y  x  5

3 x  y   2
inequalities.
23. ________________________ occur on
the solid boundary lines of the shaded
region.
24. Parallel lines have _____________
Solutions
25. Coinciding lines (the same two lines)
have __________________ solutions.
26. Unit 2 Review
What is the solution of 8 |2n + 8| = 16
15.
The limits or restrictions are also
called ________________________.
16.
_________________________
is a method for finding a minimum or
maximum value of some quantity,
given a set of constraints.
17. On a graph, the_____________________
contains all of the points that satisfy the
constraints.
27. Unit 2 Review
Which inequality best describes the
graph?
18. The ________________________ models a
quantity that is related to the constraint
variables.
19. The ________________________ of the
feasible region are the points where the
least and greatest values for the objective
function occur.
28. Unit 2 Review. What type of symmetry
does the absolute value parent
function have?
20. The ____________________ is the solution
to a system of equations when graphed.
29. Unit 1 Review. Over what line do
inverses reflect?
21. _________________________ occur
inside the shaded region of a system of
inequalities.
30. Unit 1 Review. What are the intercepts
for the cubic parent function?
22. _________________________ occur
outside the shaded region of a system of