Download Unit Three Algebra II Practice Test Systems of Linear Equations

Unit Three
Algebra II Practice Test
Systems of Linear Equations & Inequalities
Name______________________________________________Period_____Date______________
NON-CALCULATOR SECTION
Vocabulary: Define each word and give an example.
1.
System of Linear Inequalities
2.
Objective Function
3.
Inconsistent System of Equations
Short Answer:
4.
Explain how to tell if a linear system has one, none, or infinitely many solutions when solving it algebraically.
5.
What is the first step for solving a system of linear equations by linear combinations?
6.
Solve the equation. Check your solution(s):
7.
Write the standard form of the equation of the line that passes through the points
8.
The variables x and y vary directly, and y  25 when
Review:
3 x  1  6  24
x  15 . Write an equation that relates the variables.
Problems:
**Be sure to show all work used to obtain your answer. Circle or box in the final answer.**
9.
Graph the following linear systems and solve:
a.
2x  y  9
3x  y  1
 1, 4 and  3, 9 .
b.
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x  2y  6
2 x  4 y  12
Unit Three
Algebra II Practice Test
10. Solve the linear system using the substitution method:
Systems of Linear Equations & Inequalities
2 y  x  3
7 x  3 y  21
1
x y 5
11. Solve the linear system using the linear combinations (elimination) method: 2
x  2 y  3
1
x  3y  6
2
12. Solve the linear system (any method):
1
x  5 y  3
3
2x  3y  2z  1
13. Solve the system: x  4 y  z  7
3 x  y  3 z  2
14. Graph the system of inequalities:
x y 3
a.
2x  y  5
3x  y  5
b. y  1
x 1
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Unit Three
Algebra II Practice Test
Systems of Linear Equations & Inequalities
15. Find the minimum and maximum values of the objective function subject to the given constraints.
Objective Function: C  5 x  2 y
Constraints:
x  0 2 x  y  10
y  2 x  3 y  3
16. A store sells two brands of CD players. To meet customer demand, it is necessary to stock at least twice as many CD
players of brand A as of brand B. It is also necessary to have at least 10 of brand B available. In the store there is room
for no more than 50 players. Write a system of inequalities to describe the ways to stock the two brands.
Multiple Choice Questions: Circle the best answer.
17. Solve the following linear system.
5x  2 y  8
5
y  x3
2
A.
B.
 0, 4
 0, 4
C. Infinitely many solutions
D. No solution
18. What is the x-coordinate of the solution to the following system of equations?
2x  y  z  5
x  3 y  14
2 x  3 y  2 z  2
A. 14
B. 5
C. 1
D. 2
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Unit Three
Algebra II Practice Test
Systems of Linear Equations & Inequalities
19. Using linear programming procedures, the equation C  4 x  7 y is to be maximized subject to the following
constraints:
x0
y0
x y2
3 x  4 y  8
2 y  5 x  10
The grid may be used to sketch the feasible region.
What is the minimum value for the objective function?
A. 51
B. 14
C. 8
D. 0
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Unit Three
Algebra II Practice Test
Systems of Linear Equations & Inequalities
Name______________________________________________Period_____Date______________
CALCULATOR SECTION
20. A ballet company says that 540 tickets have been sold for its upcoming performance. Tickets for the Orchestra seats are
$56. Tickets for the Balcony seats are $38. The company has sold $24,120 in tickets. How many Orchestra and Balcony
seats were sold?
21. Solve the linear system using your graphing calculator:
3x  4.02 y  9
y  3.1x  30.8
22. You are sewing doll clothes to sell at a craft show. Party dresses take 2.5 hours to make while casual sets take 1 hour.
You make a profit of $9.00 on each party dress and $4.00 on each casual set. If you have no more than 30 hours
available to sew and can make at most 15 outfits to sell, how many of each kind should you sew to maximize your
profit?
Objective Function:
Constraints:
Vertices of Feasible Region:
Maximum Profit:
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