Download Chapter 6 Review - Belle Vernon Area School District

Chapter 7 Algebra 1 Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1.
Tom has a collection of 30 CDs and Nita has a collection of 18 CDs. Tom is adding 1 CD a month to
his collection while Nita is adding 5 CDs a month to her collection. Write and graph a system to find the
number of months after which they will have the same number of CDs. Let x represent the number of months
and y the number of CDs.
a.
c.
y
50
50
45
45
40
40
35
Number of CDs
Number of CDs
y
(3, 33)
30
25
20
15
35
30
20
15
10
10
5
5
0
0
1
2
3
4
5
6
7
8
9
10
(1, 31)
25
0
x
0
1
2
Number of Months
3 months
4
5
6
7
8
9
10
x
8
9
10
x
1 month
b.
d.
y
50
50
45
45
40
40
Number of CDs
Number of CDs
y
35
30
(2, 28)
25
20
15
35
25
20
15
10
5
5
0
1
2
3
4
5
6
7
Number of Months
8
9
10
x
(3, 33)
30
10
0
____
3
Number of Months
0
0
1
2
3
4
5
6
7
Number of Months
2 months
33 months
2. By what number should you multiply the first equation to solve using elimination?
–3x – 2y = 2
–9x + 3y = 24
a. 6
b. –9
c. –3
d. 3
____
3. The sum of two numbers is 82. Their difference is 24. Write a system of equations that describes this
situation. Solve by elimination to find the two numbers.
a. x + y = 82
c. x + y = 24
x – y = 24
y – x = 82
48 and 24
48 and 30
b. x – y = 82
d. x + y = 82
x + y = 24
x – y = 24
52 and 30
53 and 29
____
4. Find a solution to the following system of equations.
a. (–8, –15)
b. (–2, –15)
c. (0, 1)
d. (2, 5)
Find a solution of the system of linear inequalities.
____
5.
a. (1, 2)
____
____
____
b. (0, –1)
c. (2, 17)
d. (–2, –5)
Use the systems of linear equations below to find the number of hours of babysitting (h) after which Nolan
and Claire will have the same amount of money (m).
6. m = 6h + 15
m = 8h + 9
a. 2 hours
b. 3 hours
c. 4 hours
d. 5 hours
7. Samantha and Maria purchased flowers. Samantha purchased 5 roses for x dollars and 4 daisies for y dollars
and spent $32 on her flowers. Maria purchased 1 rose for x dollars and 6 daisies for y dollars and spent a
total of $22. Which statement is true?
a. A rose costs $1 more than a daisy
b. Samantha spent more on daisies than roses.
c. Samantha spent more on daisies than roses.
d. Samantha spent over 4 times as much on daisies as roses.
How many solutions does the linear system have?
8. -8x – 3 y = 24
3y + 8x = -24
a. none
b. exactly one
c. two
d. Infinitely many
Open – Ended:
Solve the system of equations using substitution. Circle your answer.
9. y = 6x - 11
-2x -3y = -7
10.
-5x + y = -2
-3x + 6y = -12
Solve the system using elimination.
11. -4x + 9y = 9
x – 3y = –6
12.
5x + 8y = –29
7x – 2y = –67
Graph each system. Tell whether the system has no solution, one solution, or infinitely many solutions.
13.
y = -4x + 3
y = -4x – 2
14.
2y = 2x + 8
y–4=x
16.
6x + 8y < 32
-4x + 6y ≤ 24
Solve the system of linear inequalities by graphing.
15.
y < -x + 2
y > -x + 5