AnswersDRHS-GA-Algebra Concepts and Connections AModeling with Two-Variable Linear Inequalities

Modeling with Two-Variable Linear Inequalities — Unit test Answers

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On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (2, negative 1). Everything to the left of the line is shaded.

Question illustration
A
y > 2x + 3
B
y < 2x + 3
C
y > −2x + 3
D
y < −2x + 3
2
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Ori needed at least $1.47 in postage to mail an envelope to his cousin overseas. If x represents the number of $0.44 cent stamps he has and y represents the number of $0.10 cent stamps he has, the inequality representing the number of stamps he can use to mail the envelope is 0.44x+0.10y≥1.47.

A
1
B
2
C
3
D
5
3

The math team wraps gifts as a way to raise money for traveling to competitions. They offer two choices: a plain wrapping or a decorative wrapping with bows. The table represents the money raised over a busy shopping weekend.

Question illustration
A
The team charged $1 to wrap a gift with no bow and $2 to wrap a gift with a bow.
B
The team charged $2 to wrap a gift with no bow and $3 to wrap a gift with a bow.
C
The team charged $3 to wrap a gift with no bow and $4 to wrap a gift with a bow.
D
The team charged $4 to wrap a gift with no bow and $5 to wrap a gift with a bow.
4

What is the solution to the system of equations?y = 2x – 3.5x – 2y = –14

A
(–7, 3.5)
B
(3.5, –7)
C
(7, 10.5)
D
(10.5, 7)
5

A system of equations has infinitely many solutions. If 2y – 4x = 6 is one of the equations, which could be the other equation?

A
y = 2x + 6
B
y = 4x + 6
C
–y = –2x – 3
D
–y = –4x + 6
6

What is the x-value of the solution to the system of equations?5x + 4y = 82x − 3y = 17

A
−3
B
−2
C
4
D
5
7

Which is true about the solution to the system of inequalities shown?y > 3x + 1y < 3x – 3

Question illustration
O
Only values that satisfy y > 3x + 1 are solutions.
O
Only values that satisfy y < 3x – 3 are solutions.
V
Values that satisfy either y > 3x + 1 or y < 3x – 3 are solutions.
T
There are no solutions.
8

y = 5x + 23x = –y + 10

A
(–4, –18)
B
(–18, –4)
C
(7, 1)
D
(1, 7)
9

The table can be used to determine the solution of equations, 2x − 2y = 6 and 4x + 4y = 28.Which solution can be used to fill in both blanks in the table?

Question illustration
A
(2, 5)
B
(5, 2)
C
(5, −8)
D
(−8, 5)
10

What is the y-value of the solution to the system of equations?3x + 5y = 17x + 4y = −13

A
−3
B
−1
C
2
D
5
11

The table can be used to determine the solution to the system of equations, 2y − x = 8, and y − 2x = −5.Which solution can be used to fill in both blanks in the table?

Question illustration
A
(1, 6)
B
(6, 1)
C
(7, 6)
D
(6, 7)
12

Shawn and Dorian rented bikes from two different rental shops. The prices in dollars, y, of renting bikes from the two different shops for x hours is shown.Shop Shawn used: y=10+3.5xShop Dorian used: y=6x

A
3
B
4
C
14
D
24
13

2x + 4y = 12y = x – 3

Question illustration
A
(–1, 8)
B
(8, –1)
C
(5, StartFraction one-half EndFraction)
Option C
D
(StartFraction one-half EndFraction, 5)
Option D
14

The questions in the first section on a test are worth 3 points and the questions in the second section are worth 5 points. Let x represent the number of correct questions from the first section, and let y represent the number of correct questions from the second section. Sydney earned more than 80 points on the test. The inequality representing her score is 3x+5y>80.

A
1
B
2
C
7
D
8
15

Which statements are true about the graph of the system of linear inequalities? Select two options.y > 3x – 4y 3x − 4 has shading above a dashed line.The graph of y < x + 1 has shading below a dashed line.The graphs of the inequalities will intersect.There are no solutions to the system.The graphs of the two inequalities intersect the y-axis at (0, 1) and (0, 4).

Question illustration
A
The graph of y > 3x − 4 has shading above a dashed line.
B
The graph of y < x + 1 has shading below a dashed line.
Option B
C
The graphs of the inequalities will intersect.
D
There are no solutions to the system.
E
The graphs of the two inequalities intersect the y-axis at (0, 1) and (0, 4).

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