Question

3y <= -2x+18

Answer 1

Answer:

• A (-4, -3)
• C (2, 4)
• E (3, 2)

Step-by-step 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.

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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.

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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.