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Algebra I Test
Unit Eight – Systems of Linear Equations and Inequalities
Good Luck To______________________________________________Period_____Date____________
NON-CALCULATOR SECTION
Vocabulary: Define each word and give an example.
1.
Solution of a System of Linear Equations
2.
Parallel Lines
Short Answer:
3.
Explain how to tell if a linear system has one, none, or infinitely many solutions when solving it graphically.
4.
What is the first step for solving a system of linear equations by substitution?
5.
Solve the equation. Check your solution(s):
6.
Write the standard form of the equation of the line that passes through the points
7.
The variables x and y vary directly, and y  30 when
Review:
4 2 x 1  3  27
 2,1 and  4,8 .
x  8 . 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.**
8.
Graph the following linear systems and solve:
a.
2 x  y  5
x  2y  0
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b.
2x  y  5
4 x  2 y  10
McDougal Littell: 7.1 – 7.6
2 y  x  10
9.
Solve the linear system using the substitution method:
y
1
x3
2
10. Solve the linear system using the linear combinations (elimination) method:
2x  3y  2
5 x  2 y  16
11. Solve the linear systems (any method) and state how many solutions the system has. Then tell whether the lines are
intersecting, parallel, or coincident.
a.
3 x  12 y  30
x  4 y  10
b.
12a  3b  16
36a  9b  32
Number of Solutions: ___________________
Number of Solutions: ___________________
Type of Lines: ________________________
Type of Lines: ________________________
12. Graph the system of inequalities:
a.
3x  y  3
x y 8
b. y  2 x
x  y 1
y4
Page 2 of 5
McDougal Littell: 7.1 – 7.6
13. Your class has rented buses for a field trip. Each bus seats 44 passengers. The rental company’s policy states that you
must have at least 3 adult chaperones on each bus. Let x represent the number of students on each bus. Let y represent the
number of adult chaperones on each bus. Write a system of linear inequalities that shows the various numbers of students
and chaperones that could be on each bus.
Multiple Choice Section: Circle the best answer.
14. What is the x-coordinate of the point of intersection for the two lines below?
x  2 y  2
y  6 x  40
82
13
42
B. 
13
C. 6
D. 7
A.

15. How many solutions does the system of equations have?
x  4y  4
4 x  2 y  8
A.
B.
C.
D.
no solution
one solution
two solutions
infinitely many solutions
16. Karla is 3 times as old as Lauren. In 4 years, the sum of their ages will be 56. Which system of linear equations can be
used to find the age of Karla (k) and Lauren (l)?
k  3l

4k  4l  56
l  3k
B. 
4l  4k  56
A.
 k  3l

 k  4    l  4   56
l  3k
D. 
l   k  4   56
C.
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McDougal Littell: 7.1 – 7.6
17. Which system of inequalities is shown in the graph below?
y 1

 y  2 x  2
y 1
B. 
 y  2 x  2
y 1
C. 
 y  2x  2
y 1
D. 
 y  2x  2
A.
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McDougal Littell: 7.1 – 7.6
Algebra I Test
Unit Eight – Systems of Linear Equations and Inequalities
Good Luck To______________________________________________Period_____Date____________
CALCULATOR SECTION
18. You work at a grocery store. Your hourly wage is greater after 6:00 P.M. than it is during the day. One week you work
20 daytime hours and 20 evening hours and earn $280. Another week you work 30 day time hours and 12 evening hours
and earn a total of $276. Write a system of equations and then solve to find your daytime and evening rate.
19. Solve the linear system using your graphing calculator:
.02 x  7 y  50.8
y  6.1x  1.007
20. Selling frozen yogurt at a fair, Sam makes $565 and uses 250 cones. A single-scoop cone costs $2 and a double-scoop
cone costs $2.50. How many of each type of cone did Sam sell?
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McDougal Littell: 7.1 – 7.6