Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Match the system with the appropriate graph.
1)
A system with solution (3, 6)
1)
A)
B)
C)
D)
1
2)
A system with solution (6, 8)
2)
A)
B)
C)
D)
2
3)
A system with infinitely many solutions
3)
A)
B)
C)
D)
3
4)
A system with no solution
4)
A)
B)
C)
D)
Solve.
5)
A plane flying with a tailwind flew at a speed of 430 mph, relative to the ground. When flying
against the tailwind, it flew at a speed of 320 mph. Express these relationships as equations. Let x
represent the speed of the plane in calm air and let y represent the speed of the wind.
5)
A)
x + y =320
y =430
B)
x + y =320
x – y =430
C)
x + y =430
y =320
D)
x + y =430
x – y =320
6)
An investment was split so that part was invested at an annual rate of interest of 7% and then $5000
more than twice this amount was invested at 12%. If the total annual earnings were $4940, how
much money was invested at 12%?
6)
A)
$33,000
B)
$15,000
C)
$3300
D)
$28,000
4
Solve the system by graphing.
7)
2= 3x – y
y = 3x
7)
A)
(0, 2)
B)
Infinitely many solutions
C)
(2, 0)
D)
No solution
Solve by graphing.
8)
2x – y =0
–6x + 3y = –6
8)
A)
(–3, 4)
B)
Infinitely many solutions
C)
No solution
D)
(3, 4)
Solve by substitution and check.
9)
7x + 7y =7
–4x + 4y =12
9)
A)
(–1, 2)
B)
(–1, 3)
C)
(–2, 3)
D)
No solution
Solve by elimination and check.
10)
–6x + 3y =4
–6x + 3y =20
10)
A)
(12, –24)
B)
No solution
C)
Infinitely many solutions
D)
(–24, 12)
5
Solve.
11)
The following table gives nutritional information for a single serving of tuna and of ham:
Tuna, canned
(3 ounces) Ham, deli slices
(3 ounces)
Fat (grams) 3 3
Calories 109 120
How many servings of tuna and of ham would it take to get 15 grams of fat and 578 calories?
11)
A)
2 serving(s) of tuna, 3 serving(s) of ham
B)
3 serving(s) of tuna, 2 serving(s) of ham
C)
3 serving(s) of tuna, 3 serving(s) of ham
D)
2 serving(s) of tuna, 4 serving(s) of ham
Graph the system of linear inequalities.
12)
2x + y
4
x – 1 > 0
12)
A)
B)
6
C)
D)
Solve by elimination and check.
13)
x – y =7
7x =7y – 49
13)
A)
Infinitely many solutions
B)
(4, 3)
C)
No solution
D)
(0, 0)
Solve.
14)
Gary has to choose between two calling plans for his local phone service. Plan A charges a monthly
fee of $45 regardless of how many local calls are placed. Plan B charges $15 per month plus $0.50
for each local call placed. Express each plan’s price structure, y, in terms of number of calls placed,
x.
14)
A)
Plan A: y =15
Plan B: y = 0.50x +45
B)
Plan A: y =45
Plan B: y =15x + 0.50
C)
Plan A: y =45
Plan B: y = 0.50x +15
D)
Plan A: y =45x
Plan B: y = 0.50x +15
Solve by elimination and check.
15)
x + y = –3
x – y = –11
15)
A)
No solution
B)
(7, 5)
C)
(–8, 5)
D)
(–7, 4)
Indicate whether the ordered pair is or is not a solution to the given system.
16)
2x –3y =37
5x +3y =88
(17, –1)
16)
A)
Yes
B)
No
7
Solve by graphing.
17)
x – y =4
x + y =10
17)
A)
(3, 7)
B)
(7, 3)
C)
(14, 6)
D)
(6, 14)
Solve.
18)
Howard builds patio chairs and dog houses that he sells at the local flea market. It takes him 4
hours to build a dog house and 5 hours to build a patio chair. Howard can work no more than 40
hours per week and he must produce more dog houses than chairs. Further, he wants to build at
least 7 items each week. Write a system of inequalities to describe this situation and solve the
system by graphing. Use D for the number of dog houses and P for the number of patio chairs
produced each week.
18)
8
A)
B)
C)
D)
Graph the system of linear inequalities.
19)
y x
y –x
2+ 1
19)
9
A)
B)
C)
D)
Solve by substitution and check.
20)
x – y = –2
x =2y
20)
A)
(2, 4)
B)
(–4, –2)
C)
(–2, –4)
D)
(–2, 4)
Solve.
21)
A bottle of fruit juice contains 30% water. How much water must be added to this bottle to produce
5 L of fruit juice that is 50% water? Round to the nearest tenth.
21)
A)
1.5 L
B)
3.6 L
C)
2.5 L
D)
1.4 L
Write a system of inequalities that describes the possible solutions to the problem.
22)
Matt is going to invest no more than $4000 into two accounts earning 2% and 4% simple interest.
He would like the accounts to earn at least $100 after one year. He wants to invest $2500 or less in
the account earning 4% simple interest. Write a system of inequalities to describe this situation and
solve by graphing.
22)
A)
x + y < 4000
0.02x + 0.04y > 100
y < 2500
x > 0
y > 0
B)
2x + 4y 4000
0.02x + 0.04y
100
x 2500
x 0
y 0
C)
2x + 4y 100
0.02x + 0.04y
4000
x 2500
x 0
y 0
D)
x + y 4000
0.02x + 0.04y
100
y 2500
x 0
y 0
10
Solve the system.
23)
4x + 2y = –3
x – 1 = y
23)
A)
1
6, –7
6
B)
–1
6, –7
6
C)
–1
6, 7
6
D)
1
6, 7
6
Solve by elimination and check.
24)
–5x – 3y =5
30x + 18y = –30
24)
A)
(–25, –15)
B)
Infinitely many solutions
C)
No solution
D)
(–15, –25)
Solve by graphing.
25)
y=4x +15
16x – 4y= –60
25)
A)
No solution
B)
(0, 15)
C)
(5, –5)
D)
Infinitely many solutions
Solve.
26)
How many liters (L) of a 10% alcohol solution must be mixed with 70 L of a 50% solution to get a
20% solution?
26)
A)
21 L
B)
280 L
C)
210 L
D)
28 L
Solve by substitution and check.
27)
x + 9y =54
7x + 10y =60
27)
A)
(1, 5)
B)
No solution
C)
(0, 6)
D)
(–6, 0)
Solve the problem.
28)
Bruce is a retired carpenter who builds patio chairs and dog houses that he sells at the local flea
market. It takes him 4 hours to build a dog house and 5 hours to build a patio chair. Bruce can work
no more than 40 hours per week and he must produce more dog houses than chairs. Write a system
of inequalities to describe this situation and solve the system by graphing. Use D for the number of
dog houses and P for the number of patio chairs produced in a week.
28)
11
A)
B)
C)
D)
Solve by substitution and check.
29)
x – 4y =22
6x – 5y = –1
29)
A)
(6, –6)
B)
(–6, –7)
C)
No solution
D)
(–7, –6)
12
Solve.
30)
In a local election, the ratio of votes for the winning candidate to the losing candidate was 2 to 1. If
6309 votes were cast in the election, how many votes did the winning candidate get?
30)
A)
3154 votes
B)
4206 votes
C)
2103 votes
D)
5257 votes
Graph the system of linear inequalities.
31)
3y – x 9,
y +2x 10,
y 0
31)
A)
B)
C)
D)
Solve the problem.
13
32)
Andy decides to fence off a rectangular piece of his land to use as a vegetable garden. He has 80
feet of fencing, so the perimeter of the fenced–in area cannot exceed 80 feet. The length of the
garden is to be at least 4 feet longer than the width. Write a system of inequalities that describe this
situation and solve the system by graphing.
32)
A)
B)
C)
D)
14
Write a system of inequalities that describes the possible solutions to the problem.
33)
Andy decides to fence off a rectangular piece of his land to use as a vegetable garden. He has 80
feet of fencing so the perimeter of the fenced in area cannot exceed 80 feet. The length of the garden
is to be at least 4 feet longer than the width. The width must be at least 6 feet. Write a system of
inequalities that describe this situation. Let w represent the width and l represent the length.
33)
A)
2l + 2w
80
w l + 4
l 6
B)
l + w 80
w l + 4
l 6
C)
2l + 2w
80
l w + 4
w 6
D)
l + w 80
l w + 4
w 6
Solve by substitution and check.
34)
3x + 12y =6
x = –4y –2
34)
A)
(4, 2)
B)
No solution
C)
(2, 4)
D)
Infinitely many solutions
Solve the system by substitution.
35)
6x + 9y =45
x + 8y =40
35)
A)
(0, 5)
B)
No solution
C)
(–5, 0)
D)
(1, 4)
Solve the system by elimination.
36)
2 x – y =6
3x + y =14
36)
A)
No solution
B)
(4, 2)
C)
(2, 4)
D)
(4, 3)
Provide an appropriate response.
37)
How many solutions does the graphed system appear to have?
37)
A)
The system has two solutions.
B)
The system has one solution.
C)
The system has infinitely many solutions.
D)
The system has no solution.
Solve the system by substitution.
38)
3u + v =2
2u – 3v =6
38)
A)
u = – 14
11, v =0
B)
u = – 14
11, v =12
11
C)
u =12
11, v = – 14
11
D)
u =0, v = – 14
11
15
Solve by elimination and check.
39)
2 x – y =1
4x + y =17
39)
A)
No solution
B)
(5, 3)
C)
(3, 5)
D)
(3, 6)
Write a system of inequalities that describes the possible solutions to the problem.
40)
The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. The
company can produce up to 84 rings each day, using up to 210 total man–hours of labor. It takes 3
man–hours to make one VIP ring and 7 man–hours to make one SST ring. Let x represent the
number of VIP rings, and let y represent the number of SST rings. Including the system inequalities
x 0 and y
0, find the remaining inequalities that best describe this company’s ring production.
40)
A)
x 84, y 84, 7x +3y 210
B)
x + y 84, 7x +3y 210
C)
x 84, y 84, 3x +7y 210
D)
x + y 84, 3x +7y 210
Graph the system of linear inequalities.
41)
y –x + 2
y 2
41)
A)
B)
16
C)
D)
Solve.
42)
Andrew received an inheritance of $50,000. He invested part at an annual rate of interest of 9% and
the rest at 10%. If the total annual earnings were $4700, how much money was invested at 9%?
42)
A)
$45,300
B)
$29,000
C)
$15,000
D)
$30,000
Solve the problem.
43)
Matt is going to invest no more than $4000 in two accounts earning 2% and 4% simple interest. He
would like the accounts to earn at least $100 after one year. He wants to invest $2500 or less in the
account earning 4% simple interest. Write a system of inequalities to describe this situation and
solve by graphing.
43)
17
A)
B)
C)
D)
Indicate whether the ordered pair is or is not a solution to the given system.
44)
x + y =4
x – y =6
(5, –1)
44)
A)
Solution
B)
Not a solution
Solve.
45)
Dave’s movie collection, consisting of VHS tapes and DVDs, are arranged on a storage shelf that is
38 inches in length. The VHS tapes are 1.25 inches thick, and the DVDs have a thickness of 0.5 inch.
If 52 of his movies exactly fit on the storage shelf, how many of the movies are DVDs?
45)
A)
26 DVDs
B)
16 DVDs
C)
36 DVDs
D)
33 DVDs
18
Write a system of inequalities that describes the possible solutions to the problem.
46)
The Pen–Ink Company manufactures two ballpoint pens: silver and gold. The silver requires 8
minutes in a grinder and 15 minutes in a bonder. The gold requires 3 minutes in a grinder and 2
minutes in a bonder. The grinder can be run no more than 480 minutes per day and the bonder no
more than 350 minutes per day. Let x represent the number of silver pens, and let y represent the
number of gold pens. Including the system inequalities x
0 and y 0, find the remaining
inequalities that best represent this company’s daily production of silver and gold pens.
46)
A)
8x +15y 480, 3x +2y 350
B)
8x +3y 480, 15x +2y 350
C)
x + y 480, x + y 350, x + y 830
D)
0 23x +5y 830
Solve by elimination and check.
47)
9x + 9y =144
6x + 5y =87
47)
A)
(7, 10)
B)
No solution
C)
(6, 10)
D)
(7, 9)
Solve the system by substitution.
48)
x =3y + 11
y = x – 5
48)
A)
(2, –3)
B)
(–2, –3)
C)
(–2, 3)
D)
(2, 3)
Solve the system by elimination.
49)
2p – 5q = –10.5
3p + 10q =10.5
49)
A)
p = –1.5, q =2
B)
p =1.5, q = –1.5
C)
p = –1, q =1.5
D)
p = –1.5, q =1.5
Solve.
50)
A particular computer takes 52 nanoseconds (ns) to carry out 4 sums and 6 products, and 54
nanoseconds to perform 3 sums and 7 products. How long does the computer take to carry out one
sum and one product?
50)
A)
one sum: 4 ns
one product: 6 ns
B)
one sum: 6 ns
one product: 8 ns
C)
one sum: 4 ns
one product: 8 ns
D)
one sum: 6 ns
one product: 4 ns
19
51)
Gary has to choose between two calling plans for his local phone service. Plan A charges a monthly
fee of $60 regardless of how many local calls are placed. Plan B charges $20 per month plus $0.50
for each local call placed. Graph the system to find the number of calls that would have to be
placed for the two plans to charge the same amount.
51)
A)
80 calls
B)
100 calls
C)
70 calls
D)
90 calls
Solve the system by graphing.
52)
4x + y = –17
x +2y = –6
52)
A)
(–4, –5)
B)
(–5, 3)
C)
(–4, –1)
D)
(4, –1)
Solve the system.
53)
5x =2y
–3x + y = –1
53)
A)
(–2, 5)
B)
(2, 5)
C)
(2, –5)
D)
(–2, –5)
Indicate whether the ordered pair is or is not a solution to the given system.
54)
4x + y =17
2x + 4y=26
(3, –5)
54)
A)
Yes
B)
No
20
55)
4x + y =16
2x + 4y =22
(3, 4)
55)
A)
Not a solution
B)
Solution
Solve.
56)
A quarterback throws a pass that travels 35 yards with the wind in 2.5 seconds. If he had thrown
the same pass against the wind, the football would have traveled 15 yards in 1.5 seconds. Find the
speed of the pass that the quarterback would throw if there were no wind. If necessary, round to
the nearest tenth.
56)
A)
2 yd/sec
B)
24 yd/sec
C)
6 yd/sec
D)
12 yd/sec
Solve by elimination and check.
57)
x + 8y = –58
7x + 8y = –70
57)
A)
(–1, –8)
B)
(7, –2)
C)
(–2, –7)
D)
No solution
Solve by graphing.
58)
8x + y =19
8x + y =59
58)
A)
(16, 3)
B)
Infinitely many solutions
C)
(17, –117)
D)
No solution
Solve.
59)
During a sale, a store sells red–dot items at a 40% discount and yellow–dot items at a 10% discount.
A shopper bought red– and yellow–dot items with a combined regular price of $37.00. If the total
discount was $8.50, how much did the shopper spend on each kind of item?
59)
A)
Red–dot items: $18.90
Yellow–dot items: $9.60
B)
Red–dot items: $21.00
Yellow–dot items: $16.00
C)
Red–dot items: $16.00
Yellow–dot items: $21.00
D)
Red–dot items: $9.60
Yellow–dot items: $18.90
Solve the problem.
21
60)
Matt is going to invest no more than $4000 in two accounts earning 2% and 4% simple interest. He
would like the accounts to earn at least $100 after one year. He wants to invest more than $2500 in
the account earning 4% simple interest. Write a system of inequalities to describe this situation and
solve by graphing.
60)
A)
B)
C)
D)
22
Solve by graphing.
61)
y=x –6
y= –x +16
61)
A)
(22, 10)
B)
(10, 22)
C)
(11, 5)
D)
(5, 11)
Indicate whether the ordered pair is or is not a solution to the given system.
62)
2x –8y =0
x +4y =0
(0, 0)
62)
A)
Yes
B)
No
Solve by substitution and check.
63)
2x + 8y =4
x = –4y +2
63)
A)
Infinitely many solutions
B)
(2, 4)
C)
No solution
D)
(4, 2)
23
Solve.
64)
A plane flying with a tailwind flew at a speed of 440 mph, relative to the ground. When flying
against the tailwind, it flew at a speed of 310 mph. Graph the system to find the speed of the plane
in calm air and the speed of the tailwind.
64)
A)
Speed of plane: 65 mph
Speed of tailwind: 375 mph
B)
Speed of plane: 375 mph
Speed of tailwind: 65 mph
C)
Speed of plane: 385 mph
Speed of tailwind: 55 mph
D)
Speed of plane: 55 mph
Speed of tailwind: 385 mph
Write a system of inequalities that describes the possible solutions to the problem.
65)
Bruce is a retired carpenter who builds patio chairs and dog houses, which he sells at his local flea
market. It takes him 3 hours to build a dog house and 4 hours to build a patio chair. Bruce can work
no more than 30 hours per week, and he must produce more chairs than dog houses. Write a
system of inequalities to describe this situation. Use D for the number of dog houses and P for the
number of patio chairs produced in a week.
65)
A)
P + D > 0
P + D 30
P > 0
D > 0
B)
P > D
4P +3D 30
P > 0
D > 0
C)
P D
4P +3D <30
P > 0
D > 0
D)
4P >3D
P + D 30
P > 0
D > 0
Graph the system of linear inequalities.
66)
y 3x – 3
y –3x + 9
x 4
66)
24
A)
B)
C)
D)
Solve by elimination and check.
67)
2x – 4y =7
6x + 8y =11
67)
A)
(2.5, –0.5)
B)
(2.5, 0)
C)
(3, –0.5)
D)
(–0.5, 2.5)
Solve the problem.
68)
Bruce is a retired carpenter who builds patio chairs and dog houses that he sells at the local flea
market. It takes him 4 hours to build a dog house and 5 hours to build a patio chair. Bruce can work
no more than 40 hours per week and he must produce more chairs than dog houses. Write a system
of inequalities to describe this situation and solve the system by graphing. Use D for the number of
dog houses and P for the number of patio chairs produced in a week.
68)
25
A)
B)
C)
D)
Solve.
69)
A 20% iodine solution is mixed with a 60% iodine solution to produce 4 gallons of 50% iodine
solution. How many gallons of each solution were needed?
69)
A)
B)
C)
D)
Solve the system by elimination.
70)
x – y =8
4x –4y = – 32
70)
A)
No solution
B)
(0, 0)
C)
Infinitely many solutions
D)
(6, 2)
Indicate whether the ordered pair is or is not a solution to the given system.
71)
x + y = –3
x – y =1
(–1, –2)
71)
A)
Yes
B)
No
26
Write a system of inequalities that describes the possible solutions to the problem.
72)
Matt is going to invest no more than $4000 into two accounts earning 2% and 4% simple interest.
He would like the accounts to earn at least $80 after one year. He wants to invest less than $1000 in
the account earning 4% simple interest. Write a system of inequalities to describe this situation and
solve by graphing.
72)
A)
x + y 4000
0.02x + 0.04y
80
x 0
y 1000
B)
0.02x + 0.04y – 80 4000
x 0
y 0
C)
x + y 80
0.02x + 0.04y
4000
x > 0
y 0
D)
x – y 4000
0.02x + 0.04y
80
x 0
y 0
Solve.
73)
Mark the electrician charges $100 for a house call, and then $30 per hour for labor. Sara the
electrician charges $75 for a house call, and then $50 per hour for labor. Write a cost equation for
each electrician, where y is the total cost of the electrical work and x is the number of hours of
labor.
73)
A)
Mark: y =75x +50
Sara: y =100x +30
B)
Mark: y =100x +30
Sara: y =75x +50
C)
Mark: y =50x +75
Sara: y =30x +100
D)
Mark: y =30x +100
Sara: y =50x +75
Graph the system of linear inequalities.
74)
x – 2y
2
x + y 0
74)
A)
B)
27
C)
D)
Solve.
75)
A clothing company sells jackets for $180 per jacket. The company’s fixed costs are $10,000 and the
variable costs are $170 per jacket. Use a graph to determine the break–even point for production.
75)
A)
(500, 180,000)
B)
(1000, 90,000)
C)
(500, 90,000)
D)
(1000, 180,000)
Graph the system of linear inequalities.
76)
x – y 1
x +2y 4
y 3
76)
28
A)
B)
C)
D)
Solve by graphing.
77)
4x + y =15
12x + 3y=45
77)
A)
(5, –5)
B)
No solution
C)
Infinitely many solutions
D)
(0, 15)
29
Solve.
78)
A young married couple had a combined annual income of $83,000. If the wife made $5000 more
than the husband, graph the system to find the two incomes.
78)
A)
Wife’s income: $39,000
Husband’s income: $44,000
B)
Wife’s income: $73,000
Husband’s income: $10,000
C)
Wife’s income: $44,000
Husband’s income: $39,000
D)
Wife’s income: $10,000
Husband’s income: $73,000
Solve the system by graphing.
79)
2x + y =8
2y =16 –4x
79)
A)
Infinitely many solutions
B)
(5, –2)
C)
(0, 8)
D)
No solution
Solve.
80)
There were 410 people at a school play. The admission price was $2 for adults and $1 for children.
The admission receipts were $610. How many adults and how many children attended?
80)
A)
210 adults and 200 children
B)
200 adults and 210 children
C)
105 adults and 305 children
D)
152 adults and 258 children
30
Solve the system.
81)
–6x + 9y + 51 = 0
–3x + 3y + 18 = 0
81)
A)
No solution
B)
(0, –4)
C)
(1, –5)
D)
(1, –4)
Solve.
82)
Jason made an extra $10,000 last year from a part–time job. He invested part of the money at an
annual rate of interest of 9% and the rest at 8%. If the total annual earnings were $870, how much
money was invested at 8%?
82)
A)
$3000
B)
$8000
C)
$5000
D)
$7000
83)
The annual salaries of a software engineer and a project supervisor total $191,300. If the project
supervisor makes $16,100 more than the software engineer, find each of their salaries.
83)
A)
software engineer: $103,700
project supervisor: $119,800
B)
software engineer: $71,500
project supervisor: $87,600
C)
software engineer: $71,500
project supervisor: $119,800
D)
software engineer: $87,600
project supervisor: $103,700
Solve the problem.
84)
Matt is going to invest no more than $4000 in two accounts earning 2% and 4% simple interest. He
would like the accounts to earn at least $80 after one year. He wants to invest more than $1000 in
the account earning 4% simple interest. Write a system of inequalities to describe this situation and
solve by graphing.
84)
A)
B)
31
C)
D)
Solve.
85)
At a local zoo, adult visitors must pay $3 and children pay $1. On one day, the zoo collected a total
of $1090. If the zoo had 570 visitors that day, how many adults and how many children visited?
85)
A)
155 adults and 415 children
B)
272 adults and 298 children
C)
310 adults and 260 children
D)
260 adults and 310 children
Solve by substitution and check.
86)
x + y = –4
y =3x – 4
86)
A)
(–4, 0)
B)
(–1, –4)
C)
(1, –2)
D)
(0, –4)
Solve the system.
87)
2m = –(n + 1)
4m + 2n = –2
87)
A)
m = 0, n = –2
B)
m =2, n = 0
C)
No solution
D)
Infinitely many solutions
Solve by substitution and check.
88)
2x + y = –4
y =4x – 4
88)
A)
(–4, 0)
B)
(–1, –8)
C)
(–4, 4)
D)
(0, –4)
Solve.
89)
The length, y, of the picture is double its height, x. It took molding 96 inches long to frame the
picture. Find the dimensions of the frame.
89)
A)
length: 16 in.
height: 32 in.
B)
length: 64 in.
height: 32 in.
C)
length: 32 in.
height: 64 in.
D)
length: 32 in.
height: 16 in.
32
90)
Mark the electrician charges $120 for a house call, and then $25 per hour for labor. Sara the
electrician charges $80 for a house call, and then $35 per hour for labor. Graph the system to find
the number of hours of electrical work that would be required for the two electricians to charge the
same amount.
90)
A)
4 hr
B)
3 hr
C)
3.5 hr
D)
4.5 hr
91)
A young married couple had a combined annual income of $59,000. If the wife made $7000 more
than the husband, write these relationships as a system of equations. Let x represent the husband’s
income and let y represent the wife’s income.
91)
A)
x + y =7000
y = x +59,000
B)
x – y =59,000
y = x +7000
C)
x + y =59,000
y = x +7000
D)
x + y =59,000
y =7000
Indicate whether the ordered pair is or is not a solution to the given system.
92)
x + y =3
x – y =9
(–6, –3)
92)
A)
Yes
B)
No
Solve the system by graphing the equations on a graphing calculator and estimating the point of intersection.
93)
–1.64x – 4.560y =4
9.33x + 6.38y =2
Round your solution to the nearest thousandth.
93)
A)
(–1.266, 1.080)
B)
(–1.080, 1.266)
C)
(1.080, –1.266)
D)
(1.266, 1.080)
Graph the system of linear inequalities.
33
94)
x +2y 18
2x + y 18
x 0
y 0
94)
A)
B)
C)
D)
Solve by elimination and check.
95)
x – 7y =17
–4x – 8y =4
95)
A)
(3, –2)
B)
(–3, –1)
C)
(2, –1)
D)
No solution
Solve by substitution and check.
96)
x + 2y =3
y = –4
96)
A)
(–5, –4)
B)
(–4, 11)
C)
(11, –4)
D)
(–5, 4)
34
Solve.
97)
A waiter made a deposit of $335. If his deposit consisted of 99 bills, some of them one–dollar bills
and the rest five–dollar bills, how many one–dollar bills did he deposit?
97)
A)
30 one–dollar bills
B)
59 one–dollar bills
C)
40 one–dollar bills
D)
35 one–dollar bills
Solve by substitution and check.
98)
3x +5y = 5
9x = 10 +15y
98)
A)
1
18, 1
6
B)
Infinitely many solutions
C)
No solution
D)
25
18, 1
6
Indicate whether the ordered pair is or is not a solution to the given system.
99)
4x + y = –3
2x + 4y=2
(–1, 1)
99)
A)
Yes
B)
No
Solve by graphing.
100)
x – y = –2
y=3
2x
100)
A)
(–4, 2)
B)
(6, 4)
C)
(4, 6)
D)
No solution
Solve the problem.
35
101)
Matt is going to invest no more than $4000 in two accounts earning 2% and 4% simple interest. He
would like the accounts to earn at least $80 after one year. He wants to invest less than $1000 in the
account earning 4% simple interest. Write a system of inequalities to describe this situation and
solve by graphing.
101)
A)
B)
C)
D)
36
Graph the system of linear inequalities.
102)
6y – x
8,
–y + 3x
6,
x 0
102)
A)
B)
C)
D)
Solve.
103)
Two plumbers make house calls. One charges $90 for a visit plus $40 per hour of work. The other
charges $75 per visit plus $50 per hour of work. For how many hours of work do the two plumbers
charge the same?
103)
A)
1 hr
B)
2 hr
C)
0.5 hr
D)
1.5 hr
104)
Anne and Nancy use a metal alloy that is 15% copper to make jewelry. How many ounces of an
alloy that is 10% copper must be mixed with an alloy that is 19% copper to form 45 ounces of the
desired alloy?
104)
A)
25 ounces
B)
30 ounces
C)
20 ounces
D)
22 ounces
37
Solve by graphing.
105)
–2x + 3y= –11
3x – 2y=19
105)
A)
No solution
B)
(–2, 25)
C)
(7, 1)
D)
(1, 7)
106)
2x – 3y = –12
3
2x + 2y = – 1
2
106)
A)
(–2, 3)
B)
Infinitely many solutions
C)
(–3, 2)
D)
No solution
Solve by elimination and check.
107)
3x + y = –4
4x – 3y = –5
107)
A)
(7
13, –1
13)
B)
No solution
C)
(–1
13, –17
13)
D)
(–17
13, –1
13)
Indicate whether the ordered pair is or is not a solution to the given system.
108)
x + y =9
x – y = –1
(–4, 5)
108)
A)
Solution
B)
Not a solution
Graph the system of linear inequalities.
38
109)
2x + y
4
y < 1
109)
A)
B)
C)
D)
Graph the system of inequalities.
39
110)
2x – y –1
–2x – y –9
x 5
110)
A)
B)
C)
D)
40
Solve by graphing.
111)
4x + y = –22
x +4y = –13
111)
A)
(5, –2)
B)
(–5, –6)
C)
(–6, 2)
D)
(–5, –2)
Solve.
112)
A crew team rows in a river with a current. When the team rows with the current, the boat travels
18 miles in 2 hours. Against the current, the team rows 6 miles in the same amount of time. At what
speed does the team row in still water?
112)
A)
6 mph
B)
3 mph
C)
7 mph
D)
8 mph
113)
Chris and Mary are selling tickets at their class play. Chris is selling student tickets for $1.00 each,
and Mary selling adult tickets for $5.50 each. If their total income for 23 tickets was $95.00, how
many tickets did Chris sell?
113)
A)
9 tickets
B)
21 tickets
C)
7 tickets
D)
16 tickets
41
Answer Key
Testname: C4
42
Answer Key
Testname: C4
43
Answer Key
Testname: C4
44