Question

Which system of inequalities is shown in the graph?

Answer 1

Answer: Choice A

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Explanation:

One shaded region is below the parabola, and the other shaded region is below the line. They both overlap outside the parabola, but under the straight line.

Since both shaded regions are below their respective boundaries, this means that we'll be using "less than" signs for each inequality. The solid boundary lines indicate "or equal to" is part of that as well.

Because of this, the answer is between A and D since both involve inequality signs that have "less than or equal to".

However, we can rule out choice D since the inequality $y \le x+3$ would have the boundary line $y = x+3$, and this boundary line has a positive slope. But notice how the red diagonal line slopes downward as we read from left to right. Therefore, the red line must have a negative slope. Luckily, choice A has one of the boundary lines as y = -x+3 to fit the description. So that's why choice A is the answer.