9514 1404 393
Answer:
(12, 4)
Step-by-step explanation:
The point (12, 4) is the only one in the doubly-shaded area of the graph. Of the choices offered, it is the only one that is a solution.
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I prefer to use a graphing calculator to draw the graph and plot the points. That is more interesting to me than evaluating the inequalities over and over.
Here, we find the first inequality is only satisfied by the first point. We can rewrite it so we're not messing with fractions.
y ≥ -5/6x +2
6y ≥ -5x +12 . . . . multiply by 6
5x +6y ≥ 12 . . . . . add 5x
Now, to check the points:
(12, 4) -- 5(12) +6(4) ≥ 12 . . . true
(0, -2) -- 5(0) +6(-2) ≥ 12 . . . not true
(6, -7) -- 5(6) +6(-7) ≥ 12 . . . not true
(-12, 7) -- 5(-12) +6(7) ≥ 12 . . . not true
Just to make sure, we can use the first point in the second inequality:
(12, 4) -- 4 ≤ 5(12) -1 . . . true
The point (12, 4) would be a solution to the two inequalities.
