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Answer:
G (-2, -3) is in the solution set
Step-by-step explanation:
<u>Finding the solution set</u>
You are given the boundary lines for the inequalities, but the graph does not show the solution set.
The line for inequality y < -2x -4 is the one with negative slope that extends from upper left to lower right. The relation of y to the comparison symbol is ...
y <
indicating that y-values in the solution set will be less than those on the line. The line itself is NOT included in the solution set. That is, "shading" will be below and left of the line.
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The line for inequality 2x - 4y ≤ 8 is the one with positive slope. Considering the variable with the positive coefficient, its relation to the comparison symbol is ...
x ≤
indicating that x-values in the solution set will be less than (or equal to) those on the line. The line IS included in the solution set. Shading will be above and left of the line with positive slope.
Then the doubly-shaded area is the quadrant at the left side of the X where the lines cross. The lower boundary of that is included in the set, while the upper boundary is not.
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<u>Considering the points</u>
Now that you know the location of the solution set, you can decide whether any given point is in it, or not.
Plotting the points, you find that F and G are on the boundary lines, and H and J are outside the solution set. Point F(-2, 0) is on the upper boundary line, so is not in the solution set, either.
The point listed in choice G, (-2, -3) is in the solution sets of both inequalities.
