AnswersAPSB 2025 Math Essentials-ALPModeling with Two-Variable Linear Inequalities

Modeling with Two-Variable Linear Inequalities — Unit test Answers

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21
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On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (negative 2, 3) and (0, negative 1). Everything to the left of the line is shaded. The second dashed line has a negative slope and goes through (0, 2) and (1, 0). Everything to the right of the line is shaded.

Question illustration
A
y<−2x+2
B
y>−2x+2
C
y<2x−2
D
y>2x−2
22
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Which ordered pairs make both inequalities true? Select two options. y x + 1 (–1, 3)(0, 2) (1, 2)(2, –1)(2, 2)

Question illustration
A
(–1, 3)
B
(0, 2)
C
(1, 2)
D
(2, –1)
E
(2, 2)
23

To eliminate the y terms and solve for x in the fewest steps, by which constants should the equations be multiplied by before adding the equations together?First equation: 4x − 3y = 34Second equation: 3x + 2y = 17

A
The first equation should be multiplied by 2 and the second equation by 3.
B
The first equation should be multiplied by 2 and the second equation by −3.
C
The first equation should be multiplied by 3 and the second equation by 4.
D
The first equation should be multiplied by 3 and the second equation by −4.
24

The cost of a parking permit consists of a one-time administration fee plus a monthly fee. A permit purchased for 12 months costs $660. A permit purchased for 15 months costs $810.What is the administration fee?

A
$50
B
$54
C
$55
D
$60
25

A coordinate grid with 2 lines. The first line is labeled y equals 0.5 x plus 3.5 and passes through (negative 3, 1), (negative 2.7, 2.1), and (0, 3.5). The second line is labeled y equals negative StartFraction 2 over 3 EndFraction x plus StartFraction 1 over 3 EndFraction and passes through the points (negative 4, 3), (negative 2.7, 2.1), and (StartFraction 1 over 3 EndFraction, 0).

Question illustration
A
(–2.7, 2.1)
B
(–2.1, 2.7)
C
(2.1, 2.7)
D
(2.7, 2.1)
26

Which value of m will create a system of parallel lines with no solution?y=mx-68x-4y=12

Question illustration
A
-2
B
-
Option B
C
Option
Option C
D
2
27

Which ordered pairs make both inequalities true? Select two options. y x + 1

Question illustration
A
(–1, 3)
B
(0, 2)
C
(1, 2)
D
(2, –1)
E
(2, 2)
28

y=5x – 1–15x – 3y=3

A
one solution: (0, –1)
B
one solution: (1, 4)
C
no solution
D
infinite number of solutions
29

Anatoliy has a combination of 104 nickels and quarters totaling $22. Which system of linear equations can be used to find the number of nickels, n, and the number of quarters, q, Anatoliy has?

A
n + q = 22 0.05n + 0.25q = 104
B
n + q = 104 5n + 25q = 22
C
n + q = 104 0.05n + 0.25q = 22
D
n + q = 22 5n + 25q = 104
30

A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation.x + y = 243x + 5y = 100What does the solution of this system indicate about the questions on the test?

A
The test contains 4 three-point questions and 20 five-point questions.
B
The test contains 10 three-point questions and 14 five-point questions.
C
The test contains 14 three-point questions and 10 five-point questions.
D
The test contains 20 three-point questions and 8 five-point questions.
31

A video game requires at least 4 points to advance. Each solved puzzle is worth two points. Each solved riddle is worth 1 point. If x is the number of solved puzzles and y is the number of solved riddles, which graph represents the overall equation represented by this scenario (all points may not apply to the scenario)?

A
On a coordinate plane, a solid straight line has a negative slope and goes through (0, 2) and (4, 0). Everything below the line is shaded.
Option A
B
On a coordinate plane, a solid straight line has a negative slope and goes through (0, 2) and (4, 0). Everything above the line is shaded.
Option B
C
On a coordinate plane, a solid straight line has a negative slope and goes through (0, 4) and (2, 0). Everything to the left of the line is shaded.
Option C
D
On a coordinate plane, a solid straight line has a negative slope and goes through (0, 4) and (2, 0). Everything to the right of the line is shaded.
Option D
32

Helena needs 3.5 cups of flour per loaf of bread and 2.5 cups of flour per batch of muffins. She also needs 0.75 cup of sugar per loaf of bread and 0.75 cup of sugar per batch of muffins. Helena has 17 cups of flour and 4.5 cups of sugar available for baking.

A
2 loaves of bread and 4 batches of muffins
B
3 loaves of bread and 3 batches of muffins
C
4 loaves of bread and 2 batches of muffins
D
5 loaves of bread and 1 batch of muffins
33

The graph of a system of inequalities is shown.

Question illustration
A
y > 2xx + 2y ≤ –8
B
y ≥ 2xx + 2y < –8
C
y < 2xx + 2y ≥ –8
D
y ≤ 2xx + 2y > –8
34

On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 2), and (1, negative 1). Everything to the right of the line is shaded.

Question illustration
A
(0, 2)
B
(2, 0)
C
(1, −2)
D
(−2, 1)
35

Which ordered pair is in the solution set of the system of linear inequalities?y > x – 1y < x – 1

Question illustration
A
(–5, 2)
B
(2, 2)
C
(5, 2)
D
no solution
36

Which description of the graph of the linear inequality y ≥ 7x – 4 is correct?

A
The graph will be a dashed line with a y-intercept of negative four and a slope of seven. The graph will be shaded below the line.
B
The graph will be a solid line with a y-intercept of negative four and a slope of seven. The graph will be shaded above the line.
C
The graph will be a solid line with a y-intercept of seven and a slope of negative four. The graph will be shaded below the line.
D
The graph will be a dashed line with a y-intercept of seven and a slope of negative four. The graph will be shaded above the line.
37

The cost of a parking permit consists of a one-time administration fee plus a monthly fee. A permit purchased for 12 months costs $660. A permit purchased for 15 months costs $810.What is the administration fee?

A
$50
B
$54
C
$55
D
$60
38

A wholesaler requires a minimum of 4 items in each order from its retail customers. The manager of one retail store is considering ordering a certain number of sofas, x, and a certain number of pillows that come in pairs, y. Which graph represents the overall equation represented by this scenario (all points may not apply to the scenario)?

A
Option
B
Option
C
Option
D
Option
39

The sum of two positive integers, a and b, is at least 30. The difference of the two integers is at least 10. If b is the greater integer, which system of inequalities could represent the values of a and b?

A
a + b ≥ 30 b ≥ a + 10
B
a + b ≥ 30 b ≤ a – 10
C
a + b ≤ 30 b ≥ a + 10
D
a + b ≤ 30 b ≤ a – 10
40

The system of equations can be solved using linear combination to eliminate one of the variables.2x − y = −4→10x − 5y = −203x + 5y = 59→3x + 5y = 59 13x = 39Which equation can replace 3x + 5y = 59 in the original system and still produce the same solution?

A
2x – y = –4
B
10x – 5y = –20
C
7x = 39
D
13x = 39

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