Let's go through the answer choices one by one
Choice A
Plug in (x,y) = (-3, -10.5)
3x - 2y >= 12
3(-3) - 2(-10.5) >= 12
-9 + 21 >= 12
12 >= 12
The last inequality is true, so the first inequality is true when (x,y) = (-3, -10.5)
Therefore, (-3,-10.5) is a solution
We can eliminate choice A because we are looking for non-solutions.
---------------------------------------
Choice B
Plug in (x,y) = (-1, -7)
3x - 2y >= 12
3(-1) - 2(-7) >= 12
-3 + 14 >= 12
11 >= 12
The last inequality is false, so the first inequality is false when (x,y) = (-1, -7)
Therefore, (-1,-7) is NOT a solution
The answer must be choice B since we're looking for non-solutions. Let's see what choice C and choice D have to say.
---------------------------------------
Choice C
Plug in (x,y) = (0, -6)
3x - 2y >= 12
3(0) - 2(-6) >= 12
0 + 12 >= 12
12 >= 12
The last inequality is true, so the first inequality is true when (x,y) = (0, -6)
Therefore, (0, -6) is a solution
We can eliminate choice C because we are looking for non-solutions.
---------------------------------------
Choice D
Plug in (x,y) = (2, -3)
3x - 2y >= 12
3(2) - 2(-3) >= 12
6 + 6 >= 12
12 >= 12
The last inequality is true, so the first inequality is true when (x,y) = (2, -3)
Therefore, (2, -3) is a solution
We can eliminate choice D because we are looking for non-solutions.
---------------------------------------
In summary, the final answer is choice B.
If you look at the attached graph, you'll notice that only point B is not in the shaded region (which represents the solution set). Any points on the boundary count as part of the solution.
