Unit 3 Practice Test
Algebra II
Important Questions
When is the test? What are the numbers in parenthesis?
What does a solution look like for a system of equations? For a system of inequalities?
How do you check solutions? Why do you check solutions?
When graphing systems of equations, what is important about the point of intersection?
How do you determine which method (substitution or elimination) you should use?
When do you shade up or down? When do you use have a dashed or solid line?
How do you create constraints from a word problem?
What is the vertex principle of linear programming?
Vocabulary
system, point of intersection, solution, substitution, coordinates, elimination, equation,
inequality, exclude, include, nonlinear, constraints, linear programming, feasible region,
vertex, maximize, minimize, optimize, vertex principle of linear programming, objective
function
Review Questions
3.1 Solving Systems by Graphing
Solve the system by graphing (1).
 5 x  y  9
1. 
 x  3 y  21
2 x  2 y  4
2. 
y  x  6
 x  y  10
3. 
 x  10
3.2 Solving Systems Algebraically
Solve the system by using substitution (1).
 6  3x  6 y
4. 
4 x  4  5 y
 y  2x  1
5. 
3x  y  1
x  3 y  7
6. 
2 x  4 y  24
Solve the system by elimination (1).
4 x  6 y  26
7. 
 2 x  3 y  13
6n  5m  19
8. 
3m  4m  13
9a  3d  3
9. 
 3a  d  1
 x  2 y  10
11. 
x  y  3
y  3
12. 
1
y  4 x 1
3.3 Systems of Inequalities
Graph the system (1).
 y   13 x  1
10. 
 y  2x  1
Determine the system of inequalities that is represented in the graph (1).
13.
14.
Nonlinear Systems
Solve the system by graphing (1).
Tell whether the coordinates are solutions to the system (1). {(1, 1), (-2, 0), (0, 0)}
 y  x 2
15. 
 y  2  x
 y  x  3  1
16. 
 y  x 3
 y   x 2
17. 
 y   x 3
Determine the system of inequalities that is represented in the graph (1).
Tell whether the coordinates are solutions to the system (1). {(-1,2), (1.5,1), (0,1)}
18.
19.
3.4 Linear Programming
Write the Constraints (1)
20. Shannon wants to accessorize her outfits. She purchases bracelets for $5 and
necklaces for $12. She has $120 to spend and wants to get at least 8 new accessories.
Write the constraints of the system. You do NOT have to graph or find the answer.
21. Baseball players sold an average of 9 tickets for the Vianney Sports Auction.
Basketball players sold an average of 7 tickets. Between the two teams they want to
sell at least 200 tickets. There are no more than 50 athletes between the two teams.
Write the constraints of the system. You do NOT have to graph or find the answer.
Use the feasible region to minimize the objective function (1).
22.
P = 4x + 9y
23. R = -2x + 5y
3.6 Systems of Equations with Three Variables
Solve the system (1)
 x  y  z  1

24.  x  y  3 z  3
2 x  y  2 z  0

3a  b  c  7

25. a  3b  c  13
b  2a  1

x  y  2z  7

26. 2 x  y  z  8
x  z  5
