Download ALEKS Homework 8 - Section 4.2 #5

Homework 8 - Section 4.2 #5
Intermediate Algebra / MAT 135 Fall 2016 possible master (Prof. Fleischner)
Student Name/ID:
1. Solve the following system of equations.
3x − 8y = 3
−3x + 13y = −18
2. Solve the following system of equations.
6x + 9y = −3
6x + 5y = 9
3. Solve the following system of equations.
−7x − 6y = −2
−9x − 4y = 16
4. Solve the following system of equations.
7x − 2y = −9
4x − 5y = −9
ALEKS Homework 8 - Section 4.2 #5 - 04/30/2016 12:44 PM EDT - Copyright © 2016 UC Regents and ALEKS Corporation.
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5. Solve the following system of equations.
−
1
1
x+ y=6
3
6
3
1
x + y = −10
4
2
6. Solve the following system of equations.
1
1
x − y = −11
2
5
4x −
1
2
y=
3
3
7. Solve the following system of equations.
−0.4x + 0.3y = 3
0.6x + 1.8y = −9
8. Solve the following system of equations.
−0.35x + 0.23y = 0.13
0.07x + 0.04y = −0.37
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9. Two systems of equations are given below.
For each system, choose the best description of its solution.
If applicable, give the solution.
The system has no solution.
−4 x + y = −8
4x − y = 8
The system has a unique solution:
x, y
=
,
The system has infinitely many solutions.
They must satisfy the following equation:
y =
The system has no solution.
4x − y = 4
−4 x + y = 4
The system has a unique solution:
x, y
=
,
The system has infinitely many solutions.
They must satisfy the following equation:
y =
ALEKS Homework 8 - Section 4.2 #5 - 04/30/2016 12:44 PM EDT - Copyright © 2016 UC Regents and ALEKS Corporation.
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10. Two systems of equations are given below.
For each system, choose the best description of its solution.
If applicable, give the solution.
The system has no solution.
x + 5y = 5
−x − 5 y = 5
The system has a unique solution:
x, y
=
,
The system has infinitely many solutions.
They must satisfy the following equation:
y =
The system has no solution.
x + 3y = 3
−x − 3 y = −3
The system has a unique solution:
x, y
=
,
The system has infinitely many solutions.
They must satisfy the following equation:
y =
11. One month Deandre rented 5 movies and 3 video games for a total of $27. The next month he
rented 2 movies and 12 video games for a total of $81. Find the rental cost for each movie and each
video game.
12. A party rental company has chairs and tables for rent. The total cost to rent 5 chairs and 2 tables
is $22. The total cost to rent 3 chairs and 8 tables is $71. What is the cost to rent each chair and
each table?
35
ALEKS Homework 8 - Section 4.2 #5 - 04/30/2016 12:44 PM EDT - Copyright © 2016 UC Regents and ALEKS Corporation.
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13. A family has two cars. The first car has a fuel efficiency of 35 miles per gallon of gas and the
second has a fuel efficiency of 25 miles per gallon of gas. During one particular week, the two cars
went a combined total of 1700 miles, for a total gas consumption of 60 gallons. How many gallons
were consumed by each of the two cars that week?
First car:
Second car:
14. The Nguyen family and the Green family each used their sprinklers last summer. The water
output rate for the Nguyen family's sprinkler was 40 L per hour. The water output rate for the Green
family's sprinkler was 25 L per hour. The families used their sprinklers for a combined total of 55
hours, resulting in a total water output of 1825 L. How long was each sprinkler used?
Nguyen family's sprinkler:
Green family's sprinkler:
15. A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 9%
vinegar, and the second brand contains 14% vinegar. The chef wants to make 330 milliliters of a
dressing that is 13% vinegar. How much of each brand should she use?
First brand:
_____ milliliters
Second brand: _____ milliliters
16. A chemical company makes two brands of antifreeze. The first brand is 45% pure antifreeze, and
the second brand is 90% pure antifreeze. In order to obtain 120 gallons of a mixture that contains
75% pure antifreeze, how many gallons of each brand of antifreeze must be used?
First brand:
_____ gallons
Second brand: _____ gallons
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17. Two systems of equations are given below.
For each system, choose the best description of its solution.
If applicable, give the solution.
The system has no solution.
−x − 3 y = 6
x + 3y = 6
The system has a unique solution:
x, y
=
,
The system has infinitely many solutions.
They must satisfy the following equation:
y =
The system has no solution.
x + 3y = 9
−x − 3 y = −9
The system has a unique solution:
x, y
=
,
The system has infinitely many solutions.
They must satisfy the following equation:
y =
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18. Two systems of equations are given below.
For each system, choose the best description of its solution.
If applicable, give the solution.
The system has no solution.
−x + 3 y = 9
x − 3y = 9
The system has a unique solution:
x, y
=
,
The system has infinitely many solutions.
They must satisfy the following equation:
y =
The system has no solution.
x − 2y = −8
−x + 2 y = 8
The system has a unique solution:
x, y
=
,
The system has infinitely many solutions.
They must satisfy the following equation:
y =
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Homework 8 - Section 4.2 #5 Answers for class Intermediate
Algebra / MAT 135 Fall 2016 possible master
1. x = −7
y = −3
2. x = 4
y = −3
3. x = −4
y=5
4. x = −1
y=1
5. x = −16
y=4
6. x = 6
y = 70
7. x = −9
y = −2
8. x = −3
y = −4
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9.
The system has no solution.
−4 x + y = −8
4x − y = 8
The system has a unique solution:
x, y
=
,
The system has infinitely many solutions.
They must satisfy the following equation:
y = 4x − 8
The system has no solution.
The system has a unique solution:
4x − y = 4
−4 x + y = 4
x, y
=
,
The system has infinitely many solutions.
They must satisfy the following equation:
y =
10.
The system has no solution.
x + 5y = 5
−x − 5 y = 5
The system has a unique solution:
x, y
=
,
The system has infinitely many solutions.
They must satisfy the following equation:
y =
The system has no solution.
x + 3y = 3
−x − 3 y = −3
The system has a unique solution:
x, y
=
,
The system has infinitely many solutions.
They must satisfy the following equation:
y = −
x
3
+
1
11. Rental cost for each movie: $1.50
Rental cost for each video game: $6.50
$1.00
ALEKS Homework 8 - Section 4.2 #5 - 04/30/2016 12:44 PM EDT - Copyright © 2016 UC Regents and ALEKS Corporation.
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12. Cost to rent each chair: $1.00
Cost to rent each table: $8.50
13. First car: 20 gallons
Second car: 40 gallons
14. Nguyen family's sprinkler: 30 hours
Green family's sprinkler: 25 hours
15. First brand:
66 milliliters
Second brand: 264 milliliters
16. First brand:
40 gallons
Second brand: 80 gallons
17.
The system has no solution.
−x − 3 y = 6
x + 3y = 6
The system has a unique solution:
x, y
=
,
The system has infinitely many solutions.
They must satisfy the following equation:
y =
The system has no solution.
x + 3y = 9
−x − 3 y = −9
The system has a unique solution:
x, y
=
,
The system has infinitely many solutions.
They must satisfy the following equation:
y = −
x
3
+
3
ALEKS Homework 8 - Section 4.2 #5 - 04/30/2016 12:44 PM EDT - Copyright © 2016 UC Regents and ALEKS Corporation.
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18.
The system has no solution.
−x + 3 y = 9
x − 3y = 9
The system has a unique solution:
x, y
=
,
The system has infinitely many solutions.
They must satisfy the following equation:
y =
The system has no solution.
x − 2y = −8
−x + 2 y = 8
The system has a unique solution:
x, y
=
,
The system has infinitely many solutions.
They must satisfy the following equation:
y =
x
2
+
4
ALEKS Homework 8 - Section 4.2 #5 - 04/30/2016 12:44 PM EDT - Copyright © 2016 UC Regents and ALEKS Corporation.
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