Question

Choose the system for the graph.

Answer 1

Answer:  Choice D

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Explanation:

The darkest shaded region is in the northern most region. This region is above both blue boundary lines.

A sample point from this region is (5,2)

We'll plug these coordinates into the first inequality of choice A

$3x+4y \le 12\\\\3(5)+4(2) \le 12\\\\23 \le 12$

which is false. So we can rule out choice A.

We can rule out choice B for the exact same reason.

The answer is between C and D

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Let's plug those x,y coordinates into the first inequality of choice C

$3x+4y \ge 12\\\\3(5)+4(2) \ge 12\\\\23 \ge 12$

which is true. So far, so good.

Now repeat for the second inequality of choice C

$2x-5y \ge 10\\\\2(5)-5(2) \ge 10\\\\0 \ge 10$

which is false. We rule out choice C. Choice D is the only thing left, so it must be the answer.

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Let's check the second inequality of choice D just for the sake of completeness

$2x-5y \le 10\\\\2(5)-5(2) \le 10\\\\0 \le 10$

which is true.

We can see that (x,y) = (5,2) makes both inequalities of choice D to be true, and therefore we have found the final answer.