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Mathematics
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May 12, 2024
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5
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FLVS ALG I
05.06 Systems of Linear Inequalities
Which of the following points lie in the solution set to the following system of inequalities?
y ≤ x − 5
y ≤ −x − 4
(1, 10)
(−1, 10)
(10, 1)
(1, −10)
Solve the following systems of inequalities and select the correct graph:
2x − y < 4
x + y > −1
In each graph, the area for f(x) is shaded and labeled A, the area for g(x) is shaded and
labeled B, and the area where they have shading in common is labeled AB.
Choose the graph that represents the following system of inequalities:
y ≥ −3x + 1
y ≥
x + 3
In each graph, the area for f(x) is shaded and labeled A, the area for g(x) is shaded and
labeled B, and the area where they have shading in common is labeled AB.
A summer camp cookout is planned for the campers and their families. There is room for 525
people. Each adult costs $9, and each camper costs $5. There is a maximum budget of
$1,200. Write the system of inequalities to represent this real-world scenario, where x is the
number of adults and y is the number of campers.
x + y ≤ 525
5x + 9y ≤ 1,200
x + y ≤ 1,200
5x + 9y ≤ 525
x + y ≤ 525
9x + 5y ≤ 1,200
x + y ≤ 1,200
9x + 5y ≤ 525
A company dyes two sizes of rugs. A small rug requires 2 hours for dyeing, and a
medium-size rug requires 3 hours for dyeing. The dyers need to make at least 15 rugs, and
they must do it in less than 60 hours. Let x equal small rugs and y equal medium rugs. Which
of the following inequalities can be paired with x + y ≥ 15 to create a system that represents
this situation?
2x + 3y < 60
3x + 2y < 60
2x + 3y > 60
3x + 2y > 60
In the graph, the area below f(x) is shaded and labeled A, the area below g(x) is shaded and
labeled B, and the area where f(x) and g(x) have shading in common is labeled AB.
The graph represents which system of inequalities?
y ≤ −2x + 3
y ≤ x + 3
y ≥ −2x + 3
y ≥ x + 3
y ≤ −3x + 2
y ≤ −x + 2
In the graph, the area below f(x) is shaded and labeled A, the area below g(x) is shaded and
labeled B, and the area where f(x) and g(x) have shading in common is labeled AB.
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