Section C Section C Checkpoint

Problem 1

Draw a graph of a system of inequalities that has no solution.

<p>A blank coordinate grid with origin 0. Each axis, 0 to 22, by 2’s.</p>

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Solution

Sample response:

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Sample Response

Sample response:

Problem 2

To have a valid password on a website, the password must have at least 2 letters, at least 1 number, and be less than 8 characters (letters or numbers) in length.

Write 3 inequalities to represent the constraints. Make sure to include what each variable represents.
Would the password j8675309 be a solution to the inequalities you wrote? Explain your reasoning.
Graph the solution region for the system of 3 inequalities.

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Solution

Sample response:

$x \geq 2, y \geq 1, x + y < 8$ where $x$ is the number of letters and $y$ is the number of numbers in the password.
No. Sample reasoning: There is only 1 letter and there are 8 characters, so $x < 2$ and $x + y = 8$ , which do not fit the constraints.

Show Sample Response

Sample Response

Sample response:

$x \geq 2, y \geq 1, x + y < 8$ where $x$ is the number of letters and $y$ is the number of numbers in the password.
No. Sample reasoning: There is only 1 letter and there are 8 characters, so $x < 2$ and $x + y = 8$ , which do not fit the constraints.