Answer:
- A (-4, -3)
- C (2, 4)
- E (3, 2)
Explanation:
It is convenient to use technology to plot the points and the functions to see what lies where. The first attachment shows such a plot.
_____
Of course, you can do the function evaluations. For example, testing answer B, we find ...
... 3·6 ≤ -2·1 +18 . . . . false for the first equation — not a solution
Checking all the points requires 10 function evaluations. When things get repetitive like that, I like to use a graphing calculator or spreadsheet.
_____
Using a calculator
The second attachment shows a calculator evaluating the viability of each point as a solution. The equations have been rearranged to ...
- -2x -3y +18 ≥ 0
- -x +4y +12 ≥ 0
This makes it easy to look at the evaluation results to see if the solution is viable or not.
The x-values of the points are entered into list L₁ and the y-values into L₂. The result of the first inequality above is in L₃ and the result for the second inequality is in L₄. Any negative value in L₃ or L₄ shows a point that is not part of the solution set. Points B and D fail to match problem requirements.
Points A, C, and E are in the solution set.