Page 1
1.
Solve the system by graphing.
4 + 24
–4 + –24
xy
xy
=
=
2.
Solve the system by elimination.
A1signA1 B1sign B1 C1
A2signA2 B2sign B2 C2
xy
xy
=
=
3.
Solve the system by elimination.
A1signA1 B1sign B1 C1
A2signA2 B2sign B2 C2
xy
xy
=
=
4.
Solve the system by elimination.
A1signA1 B1sign B1 C1
A2signA2 B2sign B2 C2
xy
xy
=
=
5.
Solve the system by elimination.
A1signA1 B1sign B1 C1
A2signA2 B2sign B2 C2
xy
xy
=
=
6.
Solve the system by elimination.
– 2 –3
3 – 8 –9
xy
xy
=
=
7.
Solve the system by substitution.
+ 6 –27
–2 + 5 –31
xy
xy
=
=
8.
Solve the system by substitution.
3 – 2 –3
– 7 –20
xy
xy
=
=
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9.
Solve the system by substitution.
–5 – –24
–5 – 4 –21
xy
xy
=
=
10.
Solve the system by substitution.
5 + 2 25
4 + 17
xy
xy
=
=
11.
Solve the system.
7–
16 +8
yx
yx
=
=
12.
Solve the system.
13.
Solve the system.
3 + 2 –14
– 4 0
xy
xy
=
=
14.
Solve the system.
2 + 5 –13
5 + 2 –1
xy
xy
=
=
If the system is either inconsistent or dependent, enter either inconsistent or dependent.
15.
Solve the system.
–4 – 8 17.6
–5 + 5 –20
xy
xy
=
=
If the system is either inconsistent or dependent, enter either inconsistent or dependent.
16.
Solve the system of equations.
– + 1
–9 + 41
yx
yx
=
=
If the system is either inconsistent or dependent, enter either inconsistent or dependent.
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17.
Solve the system.
–18 + 9 –81
6 – 3 243
xy
xy
=
=
If the system is either inconsistent or dependent, enter either inconsistent or dependent.
18.
Determine the number of solutions of the system.
12 + 3 42
–4 – –14
xy
xy
=
=
A)
zero
B)
an infinite number
C)
one
D)
two
19.
Determine the number of solutions of the system.
4 + 2 –14
–4 – 3 15
xy
xy
=
=
A)
one
B)
an infinite number
C)
zero
D)
two
20.
A shopkeeper has two types of coffee beans on hand. One type sells for $3.20 per lb, the
other for $6.00 per lb. How many pounds of the $3.20 per lb coffee beans must be used
in the mixture to produce 55 lbs of a blend that sells for $3.62 per lb?
Round your answer to 2 decimal places.
21.
AAA Car Rental charges $44 per day plus $0.15 for each mile driven. CCC Car Rental
charges $29 per day plus $0.2 per mile driven.
A) Write a linear function that gives the cost, C, to rent a car for one day from AAA
Car Rental as a function the number of miles driven, m.
B) Write a linear function that gives the cost, C, to rent a car for one day from CCC
Car Rental as a function the number of miles driven, m.
C) How many miles must you drive in one day before AAA Car Rental is your better
choice?
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22.
A company assumes a linear relationship exists between the consumer demand for its
product and the price charged, p.
When the price of its product was $4 per unit, the weekly quantity demanded was 302
units, and when the unit price was raised to $5, the weekly quantity demanded
dropped to 296 units.
A) Write a formula for D, the weekly quantity demanded for the product when the
price per unit is p dollars.
B) Suppose also that there is a linear relationship between the quantity supplied S of
the product and the unit price. p. Suppose that the weekly quantity supplied is 254
when the price is $5 and that the quantity supplied rises by 8.4 units when the price
rises by $1.4. Write a formula for S, the weekly quantity supplied when the price of
the product is p dollars.
C) The market clearing price or equilibrium point is the price at which supply equals
demand. Find the market clearing price for the product.
23.
State whether the system of equations illustrated by each graph has “One solution”, “No
solution”, or “Infinitely many solutions”.
24.
State whether the system of equations has “One solution”, “No solution”, or “Infinitely
many solutions”.
–3x + y = 11
–2x + 3y = 12
25.
Solve the system of equations. Express the answers in fraction form if necessary.
1 1 9
5 2 20
xy+=
1 1 2
3 4 5
xy+=
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26.
Solve the system of equations. Express the answers in decimal form if necessary.
2.1x + 3.1y = 8.2
4x – 2.7y = –18.8
27.
Solve the system of equations by substitution.
y = 3x + 2z – 7
x = –4y
–
4
–5 = 2x + 2y – z
28.
Solve the system of equations using elimination.
3x + 2y – 3z = 15
2x – 3y + 4z = –15
2x – 3y – 2z = –3
29.
Matwirth wants to invest a total of $30,000 into two investments. The first investment
pays 3% interest, and the second investment pays 4.5% interest. If after 1 years, he
wants the total interest from both investments to be $1,185, how much should he invest
in each account?
30.
A large freight truck leaves the terminal at 8:00 a.m. on a cross-country run. At 9:00
a.m., it is discovered that one package was left behind at the terminal. A small truck
leaves the terminal at 9:00 a.m. to catch the large truck. If the large truck is moving at
60 miles per hour and the small truck travels at 70 miles per hour, how long (in hours)
will it take the small truck to catch the large truck?
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31.
A homeowner wishes to have a ramp built to the door of her house. If the ground
slopes up at a rate of 1 foot of rise for every 12 feet of run, and the ramp is to slope
down at a rate of 1 foot of drop for every 15 feet of run, how far away from the house
does the ramp need to start in order to reach a door that is 4.5 feet from the ground?
32.
The ski club wishes to raise money for this year’s ski competitions. The club decides to
sell shorts and t-shirts with the ski team logo for $12 for a pair of shorts and $13 for a t-
shirt. At the end of the fundraiser, 166 items had been sold and a total of $2078 had
been raised for the club. How many of each item were sold?
Slope of ramp
Slope of ground
Height
of door
Distance from house to start of ramp
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Answer Key
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