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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At an end of the year sale, Gabriela bought more than 12 bottles of hand soaps and lotions. If x represents the number of hand soaps and y represents the number of lotions she bought, which inequality best represents her purchase?

A
x + y < 12
B
x + y > 12
C
x + y ≤ 12
D
x + y ≥ 12
2
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Charlene is knitting a baby blanket. She wants its width, w, to be at least half its length, l. She estimates that she has enough yarn to put fringe around the blanket, as long as the perimeter of the blanket is no more than 180 inches. The system of inequalities shown represents the width of the blanket in inches, w, and the length in inches, l. w ≥ 0.5l2l + 2w ≤ 180

A
30 inches
B
45 inches
C
60 inches
D
90 inches
3

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
4

y=5x – 1–15x – 3y=3

A
one solution: (0, –1)
B
one solution: (1, 4)
C
no solution
D
infinite number of solutions
5

What is the value of y in the solution to the system of equations?x + y = 12x – 3y = –30

Question illustration
A
–8
B
–3
C
3
D
8
6

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
7

Two linear equations are shown.

Question illustration
A
(7, 4)
B
(7, StartFraction 13 over 3 EndFraction)
Option B
C
(8, StartFraction 14 over 3 EndFraction)
Option C
D
(9, 7)
8

A graphics company charges $50 per hour to create a logo plus $250 for the ownership rights of the logo. A private contractor charges $75 per hour to develop a logo plus a $100 supply fee.Which equation can be solved to determine x, the number of hours after which the costs would be the same?

A
50x + 250 = 75x + 100
B
50 + 250x = 75 + 100x
C
50x + 100 = 75x + 250
D
50 + 100x = 75 + 250x
9

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
10

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
11

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
12

What is the solution to this system of linear equations?3x – 2y = 14 5x + y = 32

A
(3, 5)
B
(6, 2)
C
(8, –1)
D
(14, –18)
13

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.
14

What is the solution to this system of linear equations?7x – 2y = –68x + y = 3

A
(–6, 3)
B
(0, 3)
C
(1, –5)
D
(15, –1)
15

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)
16

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
17

What is the solution to the system of equations?y = –5x + 3y = 1

A
(0.4, 1)
B
(0.8, 1)
C
(1, 0.4)
D
(1, 0.8)
18

On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 2) and (2, 0). Everything to the left of the line is shaded. The second dashed line has a negative slope and goes through (0, 2) and (4, 0). Everything below and to the left of the line is shaded.

Question illustration
A
y > x – 2 and x – 2y < 4
B
y > x + 2 and x + 2y < 4
C
y > x – 2 and x + 2y < 4
D
y > x – 2 and x + 2y < –4
19

Shirabi spent $208 on a sewing machine to make purses. She spends a total of $10 on thread, fabric, and accessories for each purse and plans to charge $36 for each purse. The equation represents her break-even point, when x represents the number of purses sold.208 + 10x = 36xHow many purses must she sell in order to break even?

A
5
B
6
C
7
D
8
20

Gillian purchased 25 books at the library book sale. Each hardcover book cost $1.50, and each paperback book cost $0.50. Gillian spent a total of $26.50. The book costs can be represented by the system of equations below. h + p = 251.50h + 0.50p = 26.50

A
11
B
12
C
13
D
14

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