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Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Identify the system of linear equations as consistent, inconsistent, or dependent. State whether the system has exactly one
solution, no solution, or an infinite number of solutions.
1)
1)
A)
inconsistent-no solution
B)
consistent-one solution
C)
dependent-infinite number of solutions
Solve the system of equations using the addition method.
2)
5x + 4y =42
5x + 2y =46
2)
A)
(-2, 10)
B)
(-10, 5)
C)
(10, -2)
D)
(-10, 4)
3)
1
2x +1
2y =1
x - y =6
3)
A)
(3, -1)
B)
(4, -2)
C)
(-4, -1)
D)
no solution
Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
4)
7x =7y + 3
7x =7y - 8
4)
A)
infinite number of solutions
B)
no solution
C)
one solution
Solve the system of equations using the addition method.
5)
4x + 2y =-30
3x - 1
4y =- 41
4
5)
A)
(-3, -8)
B)
(4, -8)
C)
(-4, -7)
D)
no solution
Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
6)
9x - 3y =9
36x - 12y =27
6)
A)
one solution
B)
infinite number of solutions
C)
no solution
Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state.
7)
6x + y = 0
-6x + y = -12
7)
A)
(-1, 6)
B)
(1, -6)
C)
(-1, -6)
D)
(1, 12)
Find the solution to the system of equations by substitution.
8)
x - 5y = -4
x + 8y = -4
8)
A)
(4, 0)
B)
(-4, 0)
C)
(0, -4)
D)
(0, 4)
Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
9)
6x + y =19
5x - 3y =12
9)
A)
infinite number of solutions
B)
no solution
C)
one solution
3
10)
3x - 2y=14
2x + 5
4y=- 1
10)
A)
one solution
B)
no solution
C)
infinite number of solutions
Find the solution to the system of equations by substitution.
11)
x + y = 0
2x + 3y = -7
11)
A)
(-7, 7)
B)
(7, -7)
C)
(-6, 6)
D)
(6, -6)
Express the exercise as a system of linear equations, then find the solution. Use a calculator where appropriate.
12)
Two cars leave town at the same time going in the same direction. One travels at 35 mph and the
other travels as 49 mph. In how many hours will they 28 mi apart?
12)
A)
14 hr
B)
2 hr
C)
35 hr
D)
1 hr
Determine if the following ordered pair satisfies the system of linear equations.
13)
1
3, 1
2;
2x =4- y
x - 10y =-3
13)
A)
Yes
B)
No
Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state.
14)
x = -y
y + x = 6
14)
A)
(1, 5)
B)
(1, 1)
C)
dependent
D)
inconsistent
Determine the solution to the system of inequalities.
15)
y 4x - 2
y >2
3x
15)
5
A)
B)
C)
D)
Identify the system of linear equations as consistent, inconsistent, or dependent. State whether the system has exactly one
solution, no solution, or an infinite number of solutions.
16)
16)
A)
inconsistent-no solution
B)
consistent-one solution
C)
dependent-infinite number of solutions
Solve the system of equations using the addition method.
17)
5x - 5y =9
10x - 10y =27
17)
A)
12
5, -12
5
B)
(9, 27)
C)
infinite number of solutions
D)
no solution
Express the exercise as a system of linear equations, then find the solution. Use a calculator where appropriate.
18)
The following graph shows that more and more people in a certain country are moving from urban
cities to the suburbs. The percent, p, of the population living in urban cities can be estimated by the
equation p = -2.4t +73 and the percent of the population living in the suburbs by the equation
p = 2.4t +3. In both equations, t represents the number of years since 2000. That is, t = 0
corresponds to 2000, t = 1 corresponds to 2001, and so on. Assuming this trend continues, use both
equations to estimate the year in which the percent of the population of this certain country living
in urban cities will be equal to the percent living in the suburbs.
73
49
27
3
18)
A)
2012
B)
2020
C)
2016
D)
2014
Solve the problem.
19)
Devon purchased tickets to an air show for 6 adults and 2 children. The total cost was $168. The
cost of a child's ticket was $4 less than the cost of an adult's ticket. Find the price of an adult's ticket
and a child's ticket.
19)
A)
adult's ticket: $24; child's ticket: $20
B)
adult's ticket: $22; child's ticket: $18
C)
adult's ticket: $23; child's ticket: $19
D)
adult's ticket: $21; child's ticket: $17
Find the solution to the system of equations by substitution.
20)
x = -y
y + x = 6
20)
A)
(1, 5)
B)
(1, 1)
C)
infinite number of solutions
D)
no solution
Express the exercise as a system of linear equations, then find the solution. Use a calculator where appropriate.
21)
A college student earned $6500 during summer vacation working as a waiter in a popular
restaurant. The student invested part of the money at 9% and the rest at 6%. If the student received
a total of $477 in interest at the end of the year, how much was invested at 9%?
21)
A)
$2900
B)
$3250
C)
$1083
D)
$3600
Determine the solution to the system of inequalities.
22)
4x + 3y 12
x
y
22)
A)
B)
9
C)
D)
Express the exercise as a system of linear equations, then find the solution. Use a calculator where appropriate.
23)
Jarod is having a problem with rabbits getting into his vegetable garden, so he decides to fence it in.
The length of the garden is 8 feet more than 3 times the width. He needs 56 feet of fencing to do the
job. Find the length and width of the garden.
23)
A)
length: 26 ft; width: 6 ft
B)
length: 23 ft; width: 5 ft
C)
length: 20 ft; width: 4 ft
D)
length: 44 ft; width: 12 ft
24)
An 8-cylinder sedan gives 18 miles per gallon in city driving and 21 miles per gallon in highway
driving. A 300-mile trip required 15.5 gallons of gasoline. How many whole miles were driven in
the city?
24)
A)
132 mi
B)
153 mi
C)
168 mi
D)
147 mi
25)
On a buying trip in Los Angeles, Rosaria Perez ordered 120 pieces of jewelry: a number of bracelets
at $9 each and a number of necklaces at $12 each. She wrote a check for $1170 to pay for the order.
How many bracelets and how many necklaces did Rosaria purchase?
25)
A)
95 bracelets and 25 necklaces
B)
90 bracelets and 30 necklaces
C)
100 bracelets and 20 necklaces
D)
85 bracelets and 35 necklaces
Determine if the following ordered pair satisfies the system of linear equations.
26)
(-1, -3)
2x =-5 - y
4x =-10 - 2y
26)
A)
Yes
B)
No
Solve the problem.
27)
A flat rectangular piece of aluminum has a perimeter of 58 inches. The length is 13 inches longer
than the width. Find the width.
27)
A)
8 in.
B)
34 in.
C)
21 in.
D)
29 in.
Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state.
28)
2x + y =9
8x + 4y =36
28)
A)
(5, -1)
B)
(0, 9)
C)
dependent
D)
inconsistent
Identify the system of linear equations as consistent, inconsistent, or dependent. State whether the system has exactly one
solution, no solution, or an infinite number of solutions.
29)
29)
A)
dependent-infinite number of solutions
B)
consistent-one solution
C)
inconsistent-no solution
Express the exercise as a system of linear equations, then find the solution. Use a calculator where appropriate.
30)
Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make 24 pounds of feed
worth $0.53 per pound by mixing one kind worth $0.37 per pound with another worth $0.91 per
pound. How many pounds of the cheaper kind should they use in the mix? Round your answer to
the nearest pound, if necessary.
30)
A)
12 lb
B)
19 lb
C)
7 lb
D)
17 lb
31)
Kelly is a partner in an Internet-based seed and garden supply business. The company offers a
blend of exotic wildflower seeds for $95 per pound and a blend of common wildflower seeds for
$30 per pound. Kelly is creating a medium-price product by mixing together 35 pounds of the
more expensive blend with 9 pounds of the less expensive blend. What will be the price per pound
for the new blend? (Round to the nearest cent, if necessary.)
31)
A)
$15.24 per pound
B)
$81.70 per pound
C)
$28.76 per pound
D)
$43.30 per pound
32)
There were 470 people at a play. The admission price was $2 for adults and $1 for children. The
admission receipts were $670. How many adults and how many children attended?
32)
A)
200 adults and 270 children
B)
167 adults and 303 children
C)
270 adults and 200 children
D)
135 adults and 335 children
Find the solution to the system of equations by substitution.
33)
x + 2y =2
8x - 9y = -9
33)
A)
(1, 0)
B)
(1, 1)
C)
(0, 1)
D)
(0, 0)
Determine the solution to the system of inequalities.
13
34)
-x + 2y -6
3x + 2y > -18
34)
A)
B)
C)
D)
14
Find the solution to the system of equations by substitution.
35)
1
2x +2
3y =32
1
4x -5
9y =40
35)
A)
(-100, -27)
B)
(-100, 27)
C)
(100, 27)
D)
(100, -27)
Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
36)
-2x - 8y =1
5x +20y = 0
36)
A)
infinite number of solutions
B)
one solution
C)
no solution
Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state.
37)
x +1
3y=-6
x=-5
37)
A)
(-5, -3)
B)
(5, -3)
C)
dependent
D)
inconsistent
Find the solution by graphing the system of equations.
38)
A shopkeeper ordered a total of 30 pounds of cashews and peanuts. He ordered 16 fewer pounds of
cashews than peanuts. We can represent this situation with the system of equations
c + p =30
p - c =16
where p represents the pounds of peanuts and c represents the pounds of cashews. How many
pounds of peanuts did he order?
38)
A)
15 lb
B)
23 lb
C)
14 lb
D)
7 lb
Solve the system of equations using the addition method.
39)
2x + 20y = -162
11x + 4y =63
39)
A)
(-9, 9)
B)
(-4, 9)
C)
(11, -11)
D)
(9, -9)
Find the solution to the system of equations by substitution.
40)
-5x + 7y =15
x + 6y =-3
40)
A)
(3, -1)
B)
(-3, 0)
C)
(-2, -3)
D)
no solution
Solve the system of equations using the addition method.
41)
x - 5y =4
8x - 6y =-36
41)
A)
(6, -1)
B)
(-7, -1)
C)
(-6, -2)
D)
no solution
Determine if the following ordered pair satisfies the system of linear equations.
42)
(-2, 5)
x + y =7
x - y =-3
42)
A)
Yes
B)
No
Find the solution to the system of equations by substitution.
43)
7x + y = 0
-7x + y = -14
43)
A)
(-1, -7)
B)
(-1, 7)
C)
(1, -7)
D)
(1, 14)
Solve the system of equations using the addition method.
44)
1
2x +1
2y =5
1
4x -1
4y =3
2
44)
A)
(7, 3)
B)
(-8, 3)
C)
(8, 2)
D)
no solution
Determine if the following ordered pair satisfies the system of linear equations.
45)
(-4, 5)
3x + y =-7
2x + 3y =7
45)
A)
Yes
B)
No
Find the solution to the system of equations by substitution.
46)
y - 5x =3
6y =30x + 18
46)
A)
(-1.5, -1)
B)
(1, 1)
C)
infinite number of solutions
D)
no solution
47)
x + 7y = -2
3x + y = 34
47)
A)
(3, 7)
B)
(-2, 3)
C)
(7, 12)
D)
(12, -2)
Express the exercise as a system of linear equations, then find the solution. Use a calculator where appropriate.
48)
Jamil always throws loose change into a pencil holder on his desk and takes it out every two weeks.
This time it is all nickels and dimes. There are 7 times as many dimes as nickels, and the value of
the dimes is $6.50 more than the value of the nickels. How many nickels and dimes does Jamil
have?
48)
A)
9 nickels and 63 dimes
B)
10 nickels and 70 dimes
C)
11 nickels and 77 dimes
D)
70 nickels and 10 dimes
Identify the system of linear equations as consistent, inconsistent, or dependent. State whether the system has exactly one
solution, no solution, or an infinite number of solutions.
49)
49)
A)
inconsistent-no solution
B)
dependent-infinite number of solutions
C)
consistent-one solution
Find the solution to the system of equations by substitution.
50)
2x + 9y = -8
x +1
3y =13
3
50)
A)
(-5, 2)
B)
(5, 2)
C)
(-5, -2)
D)
(5, -2)
Express the exercise as a system of linear equations, then find the solution. Use a calculator where appropriate.
51)
A twin-engined aircraft can fly 1008 miles from city A to city B in 4 hours with the wind and make
the return trip in 7 hours against the wind. What is the speed of the wind?
51)
A)
72 mph
B)
54 mph
C)
90 mph
D)
36 mph
Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state.
52)
x + y =7
x + y =5
52)
A)
(4, 1)
B)
(4, 3)
C)
dependent
D)
inconsistent
Express the exercise as a system of linear equations, then find the solution. Use a calculator where appropriate.
53)
A cruise boat travels 12 miles downstream in 4 hours and returns upstream in 12 hours. Find the
rate of the stream.
53)
A)
5 mph
B)
1 mph
C)
3 mph
D)
2 mph
Determine the solution to the system of inequalities.
54)
x 3
y 4
54)
A)
B)
20
C)
D)
Express the exercise as a system of linear equations, then find the solution. Use a calculator where appropriate.
55)
Mardi received an inheritance of $40,000. She invested part at 9% and the rest at 12%. Her total
annual income from the investments was $3900. Find the amount she invested at 9%.
55)
A)
$30,000
B)
$36,100
C)
$29,000
D)
$15,000
56)
A movie theater charges $8.00 for adults and $5.00 for children. If there were 40 people altogether
and the theater collected $272.00 at the end of the day, how many of them were adults?
56)
A)
16 adults
B)
10 adults
C)
24 adults
D)
29 adults
Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
57)
x + y = -24
y=-4x
57)
A)
one solution
B)
no solution
C)
infinite number of solutions
Determine if the following ordered pair satisfies the system of linear equations.
58)
9
8, 11
4
2x -3y = -6
-x +5
2=1
2y
58)
A)
Yes
B)
No
Express the exercise as a system of linear equations, then find the solution. Use a calculator where appropriate.
59)
The three angles in a triangle always add up to 180°. If one angle in a triangle is 72° and the second
is 3 times the third, what are the three angles?
59)
A)
72°, 82°, 26°
B)
72°, 79°, 29°
C)
72°, 80°, 28°
D)
72°, 81°, 27°
60)
A theatre sells two types of tickets to their plays; children's tickets and adult tickets. For today's
performance they have sold a total of 1220 tickets. Also, they have sold 4 times as many adult
tickets as children's tickets. How many adult tickets have they sold?
60)
A)
973
B)
969
C)
976
D)
982
Determine if the following ordered pair satisfies the system of linear equations.
61)
(-2, 4)
x + y =2
x - y =-6
61)
A)
Yes
B)
No
Express the exercise as a system of linear equations, then find the solution. Use a calculator where appropriate.
62)
A barge takes 4 hours to move (at a constant rate) downstream for 40 miles, helped by a current of
3 miles per hour. If the barge's engines are set at the same pace, find the time of its return trip
against the current.
62)
A)
10 hr
B)
80 hr
C)
7 hr
D)
4 hr
63)
Aviva has a total of 54 coins, all of which are either dimes or nickels. The total value of the coins is $
4.40. Find the number of each type of coin.
63)
A)
34 nickels; 20 dimes
B)
25 nickels; 29 dimes
C)
20 nickels; 34 dimes
D)
22 nickels; 32 dimes
64)
A salesman sold $350 more than the rest of the sales staff. If the sales total for the day was $1600,
how much did the rest of the sales staff sell?
64)
A)
$975
B)
$800
C)
$1250
D)
$625
Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state.
65)
y - 4x =5
2y =8x + 10
65)
A)
(1, 1)
B)
(-1.5, -1)
C)
dependent
D)
inconsistent
Solve the system of equations using the addition method.
66)
3x + 2y = -1
-3x - 8y =13
66)
A)
(-1, 2)
B)
(-3, -2)
C)
(3, 2)
D)
(1, -2)
23
Find the solution to the system of equations by substitution.
67)
x -3y =11
y =-2
67)
A)
(-2, 5)
B)
(17, -2)
C)
(-5, -2)
D)
(5, -2)
Express the exercise as a system of linear equations, then find the solution. Use a calculator where appropriate.
68)
Khang and Hector live 30.6 miles apart in southeastern Missouri. They decide to bicycle towards
each other and meet somewhere in between. Hector's rate of speed is 70% of Khang's. They start out
at the same time and meet 3 hours later. Find Hector's rate of speed.
68)
A)
6 mph
B)
4.2 mph
C)
18 mph
D)
30.6 mph
Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
69)
y - 2x =4
4y =8x + 16
69)
A)
no solution
B)
one solution
C)
infinite number of solutions
Determine if the following ordered pair satisfies the system of linear equations.
70)
(2, 12)
y =4x + 4
3y + 12x =60
70)
A)
Yes
B)
No
Solve the problem.
71)
On a buying trip in Los Angeles, Rosaria Perez ordered 120 pieces of jewelry: a number of bracelets
at $7 each and a number of necklaces at $10 each. She wrote a check for $930 to pay for the order.
How many bracelets and how many necklaces did Rosaria purchase?
71)
A)
85 bracelets and 35 necklaces
B)
95 bracelets and 25 necklaces
C)
100 bracelets and 20 necklaces
D)
90 bracelets and 30 necklaces
Find the solution to the system of equations by substitution.
72)
y =5x - 3
y =9x - 4
72)
A)
1
4, - 7
4
B)
- 7
4, 1
4
C)
infinite number of solutions
D)
no solution
Solve the problem.
73)
A bank teller has both $5 and $10 bills in her cash drawer. There are 30 $10 bills, and the total
amount of all the bills is $355. How many $5 bills are there?
73)
A)
30 $5 bills
B)
11 $5 bills
C)
13 $5 bills
D)
28 $5 bills
Express the exercise as a system of linear equations, then find the solution. Use a calculator where appropriate.
74)
The manager of a bulk foods establishment sells a trail mix for $8 per pound and premium cashews
for $12 per pound. The manager wishes to make a 320-pound trail mix-cashew mixture that will
sell for $9 per pound. How many pounds of each should be used?
74)
A)
80 lb of trail mix
240 lb of cashews
B)
240 lb of trail mix
80 lb of cashews
C)
200 lb of trail mix
120 lb of cashews
D)
160 lb of trail mix
160 lb of cashews
Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
75)
x + y = -9
x - y =13
75)
A)
no solution
B)
one solution
C)
infinite number of solutions
76)
x + 9y =29
2x + 8y =28
76)
A)
infinite number of solutions
B)
one solution
C)
no solution
Express the exercise as a system of linear equations, then find the solution. Use a calculator where appropriate.
77)
One number is four more than a second number. Two times the first number is 10 more than four
times the second number.
77)
A)
4 and 0
B)
3 and - 1
C)
- 9 and - 13
D)
2 and - 2
Solve the system of equations using the addition method.
78)
9x - 5y =7
-27x + 15y =-28
78)
A)
6
7, -10
21
B)
(3, 4)
C)
(9, 7)
D)
no solution
Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
79)
1
2x -1
2y=4
1
5x -1
5y=2
79)
A)
one solution
B)
no solution
C)
infinite number of solutions
80)
y =6x - 9
-30x + 5y =-45
80)
A)
one solution
B)
no solution
C)
infinite number of solutions
81)
5x - y = - 4
5
x + 8y = -4
81)
A)
(0, -4)
B)
(0, 4)
C)
(4, 0)
D)
(-4, 0)
82)
x + y =2
y =-2x
82)
A)
(2, 4)
B)
(-2, 4)
C)
(-2, -4)
D)
(2, -4)
27
83)
1
3x +1
3y =2
x - y =12
83)
A)
(8, -2)
B)
(-9, -2)
C)
(9, -3)
D)
no solution
Express the exercise as a system of linear equations, then find the solution. Use a calculator where appropriate.
84)
A vendor sells hot dogs and bags of potato chips. A customer buys 5 hot dogs and 2 bags of potato
chips for $13.75. Another customer buys 4 hot dogs and 3 bags of potato chips for $12.75. Find the
cost of each item.
84)
A)
$1.25 for a hot dog; $2.25 for a bag of potato chips
B)
$2.25 for a hot dog; $1.50 for a bag of potato chips
C)
$2.25 for a hot dog; $1.25 for a bag of potato chips
D)
$2.50 for a hot dog; $1.50 for a bag of potato chips
85)
Natasha rides her bike (at a constant speed) for 2 hours, helped by a wind of 3 miles per hour.
Pedaling at the same rate, the trip back against the wind takes 8 hours. Find find the total round
trip distance she traveled.
85)
A)
10 mi
B)
32 mi
C)
16 mi
D)
8 mi
Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
86)
6x + 5y =59
6x + 2y =74
86)
A)
one solution
B)
infinite number of solutions
C)
no solution
Determine the solution to the system of inequalities.
28
87)
y <4x - 2
y 3x
87)
A)
B)
C)
D)
Solve the problem.
88)
One number is 1 less than a second number. Twice the second number is 16 less than 4 times the
first. Find the two numbers.
88)
A)
10 and 11
B)
9 and 10
C)
-10 and -9
D)
8 and 9
Express the exercise as a system of linear equations, then find the solution. Use a calculator where appropriate.
89)
Doreen and Irena plan to leave their houses at the same time, roller blade towards each other, and
meet for lunch after 3 hours on the road. Doreen can maintain a speed of 6.6 miles per hour, which
is 60% of Irena's speed. If they meet exactly as planned, what is the distance between their houses?
89)
A)
52.8 mi
B)
31.68 mi
C)
33 mi
D)
19.8 mi
90)
Chandra has 5 liters of a 63% solution of sodium hydroxide in a container. What is the amount and
concentration of sodium hydroxide solution she must add to this in order to end up with 7 liters of
55% solution?
90)
A)
2 liters of 38% solution
B)
2 liters of 33% solution
C)
2 liters of 36% solution
D)
2 liters of 35% solution
Determine the solution to the system of inequalities.
91)
2x + y >2
2x + y <-1
91)
30
A)
B)
C)
no solution
D)
Determine if the following ordered pair satisfies the system of linear equations.
92)
(-2, 6)
y =4x +14
y = -3x
92)
A)
Yes
B)
No
Express the exercise as a system of linear equations, then find the solution. Use a calculator where appropriate.
93)
The following bar graph shows the cost per square yard of the same hardwood flooring at two
different stores along with the installation cost at each store.
$300
$22 $260
$16
(i) Find the number of square yards of hardwood flooring that someone must purchase for the total
cost of the hardwood flooring plus installation to be the same from both stores. Round your answer
to the nearest tenth of a square yard, if necessary.
(ii) If 35 square yards of hardwood flooring needs to be purchased, which store will be less
expensive?
93)
A)
(i) 6.7 square yards; (ii) Store A
B)
(i) 6.7 square yards; (ii) Store B
C)
(i) 9.3 square yards; (ii) Store B
D)
(i) 9.3 square yards; (ii) Store A
94)
A flat rectangular piece of aluminum has a perimeter of 58 inches. The length is 5 inches longer
than the width. Find the width.
94)
A)
17 in.
B)
29 in.
C)
12 in.
D)
22 in.
Identify the system of linear equations as consistent, inconsistent, or dependent. State whether the system has exactly one
solution, no solution, or an infinite number of solutions.
95)
95)
A)
dependent-infinite number of solutions
B)
inconsistent-no solution
C)
consistent-one solution
Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
96)
y =2x + 7
y =7x + 6
96)
A)
infinite number of solutions
B)
no solution
C)
one solution
Find the solution by graphing the system of equations.
97)
A tour group split into two groups when waiting in line for food at a fast food counter. The first
group bought 8 slices of pizza and 5 soft drinks for $37.64. The second group bought 7 slices of
pizza and 4 soft drinks for $32.38. We can represent this situation with the system of equations
8p +5s =37.64
7p +4s =32.38
where p is the cost of a slice of pizza and s is the cost of a soft drink. Determine the cost of one slice
of pizza.
97)
A)
$3.78 per slice of pizza
B)
$3.28 per slice of pizza
C)
$1.98 per slice of pizza
D)
$1.48 per slice of pizza
Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
98)
4y = x + 32
9x - 5y = -9
98)
A)
infinite number of solutions
B)
one solution
C)
no solution
Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state.
99)
1
2x - y = 1
x =2
99)
A)
(0, 2)
B)
(2, 1)
C)
2, 1
2
D)
(2, 0)
Solve the problem.
100)
A vendor sells hot dogs and bags of potato chips. A customer buys 3 hot dogs and 3 bags of potato
chips for $5.25. Another customer buys 4 hot dogs and 2 bags of potato chips for $5.50. Find the
cost of each item.
100)
A)
$1.00 for a hot dog; $0.75 for a bag of potato chips
B)
$1.00 for a hot dog; $1.00 for a bag of potato chips
C)
$1.25 for a hot dog; $1.00 for a bag of potato chips
D)
$0.75 for a hot dog; $1.00 for a bag of potato chips
Determine if the following ordered pair satisfies the system of linear equations.
101)
(-2, -6)
4x =2- y
3x =-18 - 4y
101)
A)
Yes
B)
No
Solve the system of equations using the addition method.
102)
5x +63y =63
5x -7y = -7
102)
A)
(0, 0)
B)
(1, 0)
C)
(1, 1)
D)
(0, 1)
Express the exercise as a system of linear equations, then find the solution. Use a calculator where appropriate.
103)
One number is 2 less than a second number. Twice the second number is 26 less than 5 times the
first. Find the two numbers.
103)
A)
-12 and -10
B)
10 and 12
C)
11 and 13
D)
9 and 11
Find the solution to the system of equations by substitution.
104)
x + y = -4
x - y =18
104)
A)
4, 7
B)
4, - 11
C)
7, 11
D)
7, - 11
Solve the system of equations using the addition method.
105)
2x - 5y =2
3x - 4y =2
105)
A)
- 2
7, 2
7
B)
2
7, - 2
7
C)
infinite number of solutions
D)
no solution
Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
106)
8x - 9y =-2
8x - 9y =-5
106)
A)
infinite number of solutions
B)
no solution
C)
one solution
107)
1
3x -1
4 y =1
2
3x +1
2y =3
107)
A)
no solution
B)
infinite number of solutions
C)
one solution
Solve the system of equations using the addition method.
108)
-2x + 5y =-4
15y =-12 + 6x
108)
A)
(-2, 5)
B)
(0, 0)
C)
infinite number of solutions
D)
no solution
Express the exercise as a system of linear equations, then find the solution. Use a calculator where appropriate.
109)
Two angles are supplementary if the sum of their measures is 180°. The measure of the first angle is
18°less than four times the second angle. Find the measure of each angle.
109)
A)
first angle =129.6°
second angle =50.4°
B)
first angle =50.4°
second angle =129.6°
C)
first angle =140.4°
second angle =39.6°
D)
first angle =39.6°
second angle =140.4°
Determine the solution to the system of inequalities.
36
110)
y 4x + 1
x + y -2
110)
A)
B)
C)
D)
37
Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state.
111)
y=x + 2
y=3x - 2
111)
A)
(2, 4)
B)
(4, 2)
C)
dependent
D)
inconsistent
112)
x + 3y =3
7x - 2y =-2
112)
A)
(1, 1)
B)
(0, 1)
C)
(0, 0)
D)
(1, 0)
38
Express the exercise as a system of linear equations, then find the solution. Use a calculator where appropriate.
113)
Julie and Eric row their boat (at a constant speed) 27 miles downstream for 3 hours, helped by the
current. Rowing at the same rate, the trip back against the current takes 9 hours. Find the rate of the
current.
113)
A)
4 mph
B)
2.5 mph
C)
3 mph
D)
6 mph
Find the solution to the system of equations by substitution.
114)
-2x + y =-1
-3x - 6y =36
114)
A)
(-1, -6)
B)
(-2, -5)
C)
(-5, -2)
D)
no solution
Express the exercise as a system of linear equations, then find the solution. Use a calculator where appropriate.
115)
Devon purchased tickets to an air show for 9 adults and 2 children. The total cost was $175. The
cost of a child's ticket was $6 less than the cost of an adult's ticket. Find the price of an adult's ticket
and a child's ticket.
115)
A)
adult's ticket: $19; child's ticket: $13
B)
adult's ticket: $16; child's ticket: $10
C)
adult's ticket: $18; child's ticket: $12
D)
adult's ticket: $17; child's ticket: $11
Solve the system of equations using the addition method.
116)
x + y =5
x - y =11
116)
A)
(-8, -2)
B)
(7, -2)
C)
(8, -3)
D)
no solution
39
Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state.
117)
2x + 2y =22
-2x + 4y =8
117)
A)
(5, 6)
B)
(6, 5)
C)
dependent
D)
inconsistent
Express the exercise as a system of linear equations, then find the solution. Use a calculator where appropriate.
118)
A bank teller has a total of 48 $10 bills in her cash drawer. The value of the bills is $415. How many
$5 bills are there?
118)
A)
13 $5 bills
B)
35 $5 bills
C)
33 $5 bills
D)
15 $5 bills
Solve the system of equations using the addition method.
119)
x - 2y =0
-6x - 2y = -28
119)
A)
(5, 1)
B)
(4, 2)
C)
(-2, 4)
D)
no solution
Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state.
120)
2x + y =3
2x + y =2
120)
A)
3
2, 0
B)
(1, 0)
C)
dependent
D)
inconsistent
Express the exercise as a system of linear equations, then find the solution. Use a calculator where appropriate.
121)
Two cars leave a city and head in the same direction. After 7 hours, the faster car is 63 miles ahead
of the slower car. The slower car has traveled 308 miles. Find the speeds of the two cars.
121)
A)
35 mph and 44 mph
B)
46 mph and 55 mph
C)
44 mph and 53 mph
D)
90 mph and 99 mph
Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state.
122)
y=-x + 1
y=2x + 4
122)
A)
(-2, -1)
B)
(-1, 2)
C)
dependent
D)
inconsistent
Solve the problem.
123)
Two numbers total -12, and their difference is 4. Find the two numbers.
123)
A)
- 4 and - 8
B)
-12 and 2
C)
- 5 and - 7
D)
- 6 and - 10
Solve the system of equations using the addition method.
124)
x + 4y =16
2x + 4y =12
124)
A)
(-3, -4)
B)
(-4, 5)
C)
(4, 4)
D)
no solution
Express the exercise as a system of linear equations, then find the solution. Use a calculator where appropriate.
125)
Two numbers total 2, and their difference is 14. Find the two numbers.
125)
A)
2 and 0
B)
1 and - 13
C)
8 and - 6
D)
2 and 2
Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
126)
y =5x + 5
5y + 25x =-25
126)
A)
no solution
B)
infinite number of solutions
C)
one solution
Find the solution to the system of equations by substitution.
127)
5x - 1
2y=13
2x - 5
3y=14
127)
A)
(-6, 2)
B)
(-2, -7)
C)
(2, -6)
D)
(3, -7)
Find the solution by graphing the system of equations.
128)
Megan is having her yard landscaped. She obtained an estimate from two landscaping companies.
Company A gave an estimate of $220 for materials and equipment rental plus $45 per hour for
labor. Company B gave and estimate of $310 for materials and equipment rental plus $30 per hour
for labor. We can represent this situation with the system of linear equations
c =220+45h
c =310+30h
where c is the total cost and h is the number of hours of labor. Find the number of hours of labor for
the two companies to have the same total cost.
128)
A)
10 hr
B)
6 hr
C)
5 hr
D)
9 hr
Express the exercise as a system of linear equations, then find the solution. Use a calculator where appropriate.
129)
A retired couple has $180,000 to invest to obtain annual income. They want some of it invested in
safe Certificates of Deposit yielding 6%. The rest they want to invest in AA bonds yielding 11% per
year. How much should they invest in each to realize exactly $17,300 per year?
129)
A)
$130,000 at 6% and $50,000 at 11%
B)
$120,000 at 6% and $60,000 at 11%
C)
$140,000 at 11% and $40,000 at 6%
D)
$130,000 at 11% and $50,000 at 6%
Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
130)
2x - 9y =4
-6x + 27y =-16
130)
A)
infinite number of solutions
B)
one solution
C)
no solution
Solve the problem.
131)
One number is four more than a second number. Two times the first number is 10 more than four
times the second number.
131)
A)
2 and - 2
B)
- 9 and - 13
C)
4 and 0
D)
3 and - 1
Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
132)
x + y = -9
x + y =-6
132)
A)
one solution
B)
infinite number of solutions
C)
no solution
133)
3y = x - 54
2x + 6y = 0
133)
A)
no solution
B)
infinite number of solutions
C)
one solution
Express the exercise as a system of linear equations, then find the solution. Use a calculator where appropriate.
134)
A chemist needs 200 milliliters of a 55% solution but has only 39% and 79% solutions available.
Find how many milliliters of each that should be mixed to get the desired solution.
134)
A)
80 ml of 39%; 120 ml of 79%
B)
120 ml of 39%; 80 ml of 79%
C)
123 ml of 39%; 80 ml of 79%
D)
123 ml of 39%; 77 ml of 79%
Solve the problem.
135)
One number is 4 less than a second number. Twice the second number is 19 more than 3 times the
first. Find the two numbers.
135)
A)
-12 and -8
B)
-11 and -7
C)
7 and 11
D)
-10 and -6
Determine the solution to the system of inequalities.
136)
x -6
y <-3
136)
A)
B)
45
C)
D)
Express the exercise as a system of linear equations, then find the solution. Use a calculator where appropriate.
137)
Dmitri needs 5 liters of a 18% solution of sulfuric acid for a research project in molecular biology.
He has two supplies of sulfuric acid solution: one is an unlimited supply of the 20% solution and
the other an unlimited supply of the 15% solution. How many liters of each solution should Dmitri
use?
137)
A)
20% solution: 3.5 liters; 15% solution: 1.5 liters
B)
20% solution: 2 liters; 15% solution: 3 liters
C)
20% solution: 2.5 liters; 15% solution: 2.5 liters
D)
20% solution: 3 liters; 15% solution: 2 liters
Solve the problem.
138)
Jamil always throws loose change into a pencil holder on his desk and takes it out every two weeks.
This time it is all nickels and dimes. There are 3 times as many dimes as nickels, and the value of
the dimes is $1.25 more than the value of the nickels. How many nickels and dimes does Jamil
have?
138)
A)
6 nickels and 18 dimes
B)
4 nickels and 12 dimes
C)
15 nickels and 5 dimes
D)
5 nickels and 15 dimes
Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
139)
x + 3y =-3
-4x - 12y =12
139)
A)
one solution
B)
no solution
C)
infinite number of solutions
Determine if the following ordered pair satisfies the system of linear equations.
140)
(2, 4)
3x + y =2
2x + 3y = -8
140)
A)
Yes
B)
No
Determine the solution to the system of inequalities.
141)
x +2y >4
y 3
141)
A)
B)
47
C)
D)
Solve the problem.
142)
Jarod is having a problem with rabbits getting into his vegetable garden, so he decides to fence it in.
The length of the garden is 4 feet more than 2 times the width. He needs 62 feet of fencing to do the
job. Find the length and width of the garden.
142)
A)
length: 24 ft; width: 10 ft
B)
length: 422
3 ft; width: 191
3 ft
C)
length: 22 ft; width: 9 ft
D)
length: 20 ft; width: 8 ft
Find the solution to the system of equations by substitution.
143)
6x - 7y =-15
x - 6y =12
143)
A)
(-6, -3)
B)
(6, -2)
C)
(-7, -2)
D)
no solution
Express the exercise as a system of linear equations, then find the solution. Use a calculator where appropriate.
144)
The sum of two angles is 154°. One angle is 23° less than twice the other. Find the angles.
144)
A)
59° and 95°
B)
57° and 97°
C)
91° and 63°
D)
57° and 91°
145)
Ellen wishes to mix candy worth $1.30 per pound with candy worth $2.88 per pound to form 31
pounds of a mixture worth $2.12 per pound. How many pounds of the more expensive candy
should she use? Round your answer to the nearest pound.
145)
A)
17 lb
B)
21 lb
C)
15 lb
D)
16 lb
146)
Two angles are complementary. Twice one angle plus the other is 152°. Find the measure of each
angle.
146)
A)
62°, 118°
B)
62°, 28°
C)
67°, 23°
D)
65°, 22°
Determine the solution to the system of inequalities.
147)
2x + 3y 6
x - y
3
147)
49
A)
B)
C)
D)
50
Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state.
148)
2x + y = 0
5x + 4y = 0
148)
A)
(4, 5)
B)
(0,0)
C)
dependent
D)
inconsistent
Find the solution by graphing the system of equations.
149)
The Family Fine Arts Center charges $25 per adult and $10 per senior citizen for its performances.
On a recent weekend evening when 491 people paid admission, the total receipts were $6440. We
can represent this situation with the system of equations
a + s =491
25a +10s =6440
with a representing the adults who attended and s representing the senior citizens who attended.
How many who paid were senior citizens?
149)
A)
192 senior citizens
B)
299 senior citizens
C)
389 senior citizens
D)
102 senior citizens
Express the exercise as a system of linear equations, then find the solution. Use a calculator where appropriate.
150)
Jimmy is a partner in an Internet-based coffee supplier. The company offers gourmet coffee beans
for $15 per pound and regular coffee beans for $3 per pound. Jimmy is creating a medium-price
product that will sell for $5 per pound. The first thing to go into the mixing bin was 14 pounds of
the gourmet beans. How many pounds of the less expensive regular beans should be added?
150)
A)
69 lb
B)
71 lb
C)
70 lb
D)
72 lb
151)
Anne and Nancy use a metal alloy that is 16% copper to make jewelry. How many ounces of an
alloy that is 14% copper must be mixed with an alloy that is 20% copper to form 81 ounces of the
desired alloy?
151)
A)
54 oz
B)
32 oz
C)
56 oz
D)
27 oz
Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
152)
3x + 5y =14
x =-4y
152)
A)
infinite number of solutions
B)
one solution
C)
no solution
Determine the solution to the system of linear equations graphically. If the system is dependent or inconsistent, so state.
153)
2x + y =-5
3x + 3y =-3
153)
A)
(-4, -5)
B)
(-4, 3)
C)
(4, 3)
D)
(-1, -3)
52
Express each equation in slope-intercept form. Without graphing the equations, state whether the system of equations
has exactly one solution, no solution, or an infinite number of solutions.
154)
2x + y =7
4x + 2y =14
154)
A)
no solution
B)
one solution
C)
infinite number of solutions
53
Answer Key
Testname: C8
Answer Key
Testname: C8
Answer Key
Testname: C8
Answer Key
Testname: C8
