Name: ____________________________________ __________________Period: _______ Table #: ___
Unit 2 Homework
1
Solve.
5(3x  4)  12  73
2
Solve.
2x  12  8x  9  x  5x
3
Determine if (-1, 4) is a solution to the following
 y  3  x

system of equations: 
 6x  2y  2
4
Solve by grahing. Check your solution.

 2x  2y  4

 y  x  6
1
5
Solve by grahing. Check your solution.

y  x  5

 y  x  3
6
Solve by grahing. Check your solution.

 3y  6x  3

 x  y  7
7
Solve by grahing. Check your solution.
 y  x  0


 8x  4y  24
9
Solve by grahing. Check your solution.
 7x  y  2


 28x  4y  12
8
Solve by grahing. Check your solution.

 x  y  1

 4x  2y  2
10
Solve by grahing. Check your solution.

 2x  3y  15

 3y  2x  15
2
11
Which system of equations is accurately
represented on the graph?
13
If 12  3(x  2)  x  8, then what is the value of
x?
A
B
A
B
C
D
12
 y


 y
 y


 y

y

 y

y

 y
 3x  6
C
 3x  6
 6x  3
D
 6x  3
 3x  6
14
5
2
1

2
1
2
3
2

What are the values of x where 2 x  4  6 ?
 3x  6
 6x  3
 6x  3
Which system of equations is accurately
represented on the graph?
A
B
C
D
15
A
B
C
D

y  x

 y  x  2
 y  x  5


 y  2x  2
 y  x  6


 y  3x  2

y  x  6

 y  3x  2
Line l passes through (1, -3) and is
1
perpendicular to y  x  7. What is the
5
equation of line l?
A
B
C
D
3
x < -1
x > -7
x > -1 or x < -7
-7 < x < -1
y  5x  2
y  5x  2
y  5x  3
y  5x  3
16
Solve by substitution:
19
Solve by substitution. Check your solution.
 x  3y  7


 2x  4y  24
20
Writing: A mistake has been made in the
solution. Explain the error and how to correct
it.
y  3x  4
3x  2y  13
3x  4y = 4
y= 3x  14
A
B
C
D
17
no solution
(5, 1)
 4  2 





 2 5 

2 

Solve by substitution. Check your solution.

 3c  2d  2

 d  4
3x  2 3x  4  13
3x  6x  8  13
 3x  8  13
 3x  21
18
x  7
Solve by substitution. Check your solution.
 x  12y  68


 x  8y  12
y  3 7  4
y  21  4
y  25
Solution: x  7 and y  25
4
21
Solve the following system using all three
methods: graphing, substition, and linear
combination.
22
Solve by linear combination. Check your
solution.

 x  y  12

 x  y  2
23
Solve by linear combination. Check your
solution.

 20x  5y  120

 10x  7.5y  80
24
Solve by linear combination. Check your
solution.

 5x  2y  19

 2x  3y  0
 4x  2y  4


 4x  2y  8
(a) Graphing (check your solution)
(b) Substiution (check your solution)
(c) Linear combination (check your solution)
(d) Which method do you prefer and why?
5
25
Solve the linear system.
28
Solve. Check your solution.
 6x  10y  12


 3x  5y  6
29
Solve. Check your solution.
 2x  4y  6


 3x  6y  8
30
Solve. Check your solution.

 4x  6y  26

 3y  2x  13
31
Does the system of equations have no solution,
one solution, or many solutions? Explain how
you can tell without graphing the system.
y  x 2
2x  2y  4
3x  2y  16
26
A
B
(4, –2)
 0 2 


C
D
(12, –2)
no solution
Solve.
2x  4y  12
3x  4y  8
A
B
C
D
27
 4  1 


no solution
 20  1 


 0  3 


What is the value of x in the solution of the
following system?

 5x  3y  11

 x  12y  3.5

6y  3x  7
A
B
C
D
0.5
2
2.5
3
6
32
Which system of equations has no solution?
A
34
Which choice best describes the solution(s) of
the system of equations?
3x  2y = 2
12x  8y = 8
3x  4y  1
3x  4y  2
B
3x  4y  1
A
B
C
D
5x  6y  2
C
3x  4y  1
3x  4y  1
D
3x  4y  1
35
12x  16y  4
33
(–2, –4) is the only solution.
many solutions
(–2, 4) is the only solution.
no solution
Express each equation in slope-intercept form.
Then determine, without solving the system,
whether the system of equations has exactly one
solution, no solution, or an infinite number of
solutions.
x  2y  4
4x  2y   14
7
The school sells tickets for its annual
Segerstrom’s Got Talent Show. A presale
ticket costs $5 and at the door it costs $7.
If 245 tickets were sold and a total of
$1321 was fundraised, how many of each
ticket were sold?
36
ASB wants to host a school dance this
month. General admission for students is
$6. However, if you have an ASB card, the
ticket only costs $4. If ASB sold a total of
525 tickets and collected $2,876. How
many of regular price tickets and how
many ASB tickets did they sell?
37
Your soccer team decides to host a car
wash at a local gas station. A car wash for
a regular car is $5 and for trucks is $7. If
ythe team washed a total of 125 cars and
trucks and collected $733, how many of
regular cars and how many trucks did the
team wash?
8
38
Homer Simpson has been invited to a
donut party. Of course, he ate all of the
donuts. There were two types of donuts at
the party: chocolate and plain. Homer ate
a total of 2,100 donuts. If the host bought
$3,548 and chocolate donuts cost $2 each
while plain cost $1 each, how many of each
type of donut did Homer eat? Will you
invite Homer to your next donut party?
39
A hummingbird can beat its wings very
fast. When it is at rest, the wings beat 500
times per minute and when it is during
activity, the wings beat 1200 times per
minute. A local scientist notices that his
hummingbird beats its wings totaling
7,100 times in 10 minutes. How many
minutes at rest and how many minutes in
activity did the hummingbird go through
during the experiment?
40
Is the ordered pair (2, –4) a solution for the
inequality 2x  4y  20?
44
y  2x  7
A
 2

   3  a solution of the
 3
2 

inequality 3x  2y  5?
41
Is the ordered pair
42
Graph . y  4x  4
B
C
43
Graph. 2x  7y14
D
9
45
Graph: y  2x  4
46
Graph. x  1
A
A
B
B
C
C
D
D
10
49
47
Graph the system of linear inequalities.
y   2x  1
y  3
Graph the system of linear inequalities.
y  2x  1
y  3
A
B
48
Graph the system of linear inequalities.
y  2x  1
y  2
C
D
11
53
50
Graph the system of linear inequalities.
y x4
Write the equation of the line, in slope-intercept
form, that passes through the point (  2,  1)
and has slope 5.
y  2x  8
A
B
C
D
54
51
Tell whether the ordered pair is a solution of
the following systems.
(a)
(b)
52
Write an equation of a line that has slope –3
and y-intercept 1.
A x   3y  1
B y   3x  1
1
C y   x1
3
D y   3x  1
12
y = 5x  9
y =  5x  9
y =  5x  9
y = 5x  9
Graph the system of inequalities.
1
y  x 2
2
1
y   x 2
2
x3
55
Graph the system of inequalities.
y  2x  1
y  x3
A
56
Graph the system of inequalities.
x3
y4
A
B
B
C
C
D
D
13
57
Graph the system of inequalities.
5x  4y  20
xy
x8
58
Graph the system of inequalities.
1
y  x 2
2
1
y   x2
2
y  4
59
Graph the system of inequalities.
y  x4
y  2x  4
y  2
A
B
C
D
14
60
Graph the system of inequalities.
2x  3y  6
x  y
x  5
62
Decide if the given ordered triple is a solution
of the following system of equations.
(–1, 2, –3)
3x  4y  3z  14
4x  2y  4z  12
x  y  5z   14
63
61
Find the domain and range in set-builder
notation.
15
Solve the system of equations.
6x – 5y – 5z = 18
3x – 2y – 3z = 8
x–y+z=0
64
Solve the system of equations.
x + y + z  5
2x  y + z  1
x  2y  z  0
66
Solve the system of equations.
x + y +z  6
2x  y + z  8
x  2y  z  12
A
B
C
D
65
Solve the system of equations.
x + 2y – 4z = –12
–x + z = 1
x+ y +z = 4
16
(–2, 2, 6)
(–6, –2, 2)
(6, 2, –2)
(2, –2, –6)
67
Solve the system of equations.
2x + y – z = –1
x – 2y = –7
x+y+z = 4
69
Solve the system of equations.
2x  3y  z  1
x yz  3
3x  y  z  15
68
Solve the system of equations.
x + 4y + 2z = 5
3x + 12y + 6z = 7
2x – 3y + z = 12
70
Solve the system of equations.
2x + y + 3z = 6
x + y – 3z = 4
7x + 5y – 3z = 24
17
71
Solve the system.
 2x  y  z  4


 x  3y  z  4

 3x  y  z  8

A
B
C
D
72
73
Solve the system.
 x  y  z  10


 2x  y  z  2

 x  2y  z  5

74
Solve the system.
 3x  y  2z  22


 x  5y  z  4

 x  3z

(2, 0, 0)
(1, 0, 2)
(2, 1, 1)
(2, 0, -2)
Solve the system.

 x  2y  z  14

 y  z  1

 x  3z  6

18