Answer:
a. (-2, 4) only
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Step-by-step explanation:
Let's check point A.
We have x = -2 and y = 4 pair up together.
Plug these coordinates into the first inequality.
x + 4y > 10
-2 + 4*4 > 10
-2 + 16 > 10
14 > 10
We get a true statement, so (-2,4) is in the shaded solution region of the inequality x+4y > 10.
Repeat for the other inequality.
3x - 2y < 12
3*(-2) - 2*4 < 12
-6 - 8 < 12
-14 < 12
This is also true.
The point (-2,4) is also in the shaded solution region for 3x-2y < 12
Since it's in both regions simultaneously, it satisfies the system of inequalities.
Therefore, (-2,4) is a solution to the system.
See the diagram below. Point A is in the shaded region.
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Now we need to check point B.
We have x = 3 and y = 1. Let's plug those into the 1st inequality.
x + 4y > 10
3 + 4*1 > 10
3 + 4 > 10
7 > 10
That final statement is false, so (3,1) is not in the shaded region for x+4y > 10. We don't need to check the other region since this point needs to satisfy both inequalities to be considered a solution overall.
See the diagram below. Point B is outside the shaded region.