Answer: Choice B (4,3)
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Explanation:
Lets go through the points one by one
So we'll try (5,3) first. Plug x = 5 and y = 3 into the first inequality
[tex]y > -0.5x+5\\3 > -0.5*5+5\\3 > -2.5+5\\3 > 2.5[/tex]
We get a true result so (5,3) is a solution to the first inequality. Now check the second inequality.
[tex]y \le 3x-2\\3 \le 3(5)-2\\3 \le 15-2\\3 \le 13\\[/tex]
That's also true. Therefore, the point (5,3) is a solution to the system overall.
Your teacher wants you to find a non-solution, so we must cross choice A off the list.
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Let's now try choice B. We have x = 4 and y = 3
[tex]y > -0.5x+5\\3 > -0.5*4+5\\3 > -2+5\\3 > 3[/tex]
That last inequality is false. It's not possible to have a number larger than itself (or smaller than itself). So (4,3) is not a solution to the first inequality. We don't need to check the second inequality as we found the answer.
