2.15.4 Identifying Graph Regions Included in a System’s Solution

Algebra 12.15.4 Identifying Graph Regions Included in a System’s Solution

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Access the Desmos guide PDF for tips on solving problems with the Desmos graphing calculator.

Use this information to answer questions 1 – 7.

A factory produces “widgets” and “zurls.” The combined number of widgets and zurls made each day cannot be more than 12. The maximum number of widgets the factory can produce in a day is 4.

Let $x$ be the number of widgets and $y$ be the number of zurls. $y$ be the number of zurls.

Select two inequalities that represent this situation.

$x \geq 4$
$x + y \leq 12$
$x > 4$
$x + y \geq 12$
$x \leq 4$

$x \leq 4$ and $x + y \leq 12$

Use the graphing tool or technology outside the course. Graph the equations $x = 4$ and $x + y = 12$ using the Desmos tool below.

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Compare your answer:

Graph of a system of two linear equations on a coordinate plane.

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Use the graphing tool or technology outside the course. Graph the system of inequalities that shows all the allowable numbers of widgets and zurls that the factory can produce in one day using the Desmos tool below.

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Compare your answer:

Graph of a system of two linear inequalities on a coordinate plane.

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In questions 4 – 7 answer the question:

Does the ordered pair represent an allowable combination of widgets and zurls produced in one day?

(4, 5)

Yes.

(11, 1)

No.

(4, 12)

No.

(3, 9)

Yes.

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- Authors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis, Jay Abramson, Sharon North, Amy Baldwin, Alyssa Howell
- Publisher/website: OpenStax
- Book title: Algebra 1
- Publication date: Jun 4, 2025
- Location: Houston, Texas
- Book URL: https://openstax.org/books/algebra-1/pages/about-this-course
- Section URL: https://openstax.org/books/algebra-1/pages/2-15-4-identifying-graph-regions-included-in-a-systems-solution

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