The shaded region in the figure above represents the solution set of which system of inequalities?

Rationale

0 <= x <= 2, 0 <= y <= x + 2.

The solution set represented by the shaded region corresponds to the inequalities where x is constrained between 0 and 2, and y is bounded below by 0 and above by the line y = x + 2. This accurately captures the area described in the figure.

A (-2 <= x <= 2, 0 <= y <= x + 2) YOUR ANSWER

This choice incorrectly includes negative values for x, which do not appear in the shaded region. The range for x should start at 0, eliminating any possibility of negative x-values, thus misrepresenting the solution set.

B (0 <= x <= 2, 0 <= y <= x + 2) CORRECT

This choice correctly describes the boundaries of the shaded region. The x-values are confined between 0 and 2, while y-values start from 0 up to the line defined by y = x + 2, accurately representing the constraints shown.

C (0 <= x <= 2, 2 <= y <= x + 2) YOUR ANSWER

This option misrepresents the lower boundary for y, stating that y must be at least 2. The shaded region includes y-values starting from 0, making this choice incorrect.

D (0 <= y <= 2, 0 <= x <= y + 2) YOUR ANSWER

Here, the inequalities incorrectly suggest that x is dependent on y, which is not the case. The shaded region does not restrict x in relation to y in this manner, thus failing to reflect the proper solution set.

E (0 <= x, 0 <= y <= x + 2) YOUR ANSWER

Although this choice correctly shows y bounded by x + 2, it fails to limit x to a maximum of 2. Without this upper boundary, the solution set expands beyond the shaded region depicted.

Conclusion

The correct representation of the shaded region is given by the inequalities 0 <= x <= 2 and 0 <= y <= x + 2, which accurately highlights the constraints on x and y. Other options either misstate the boundaries or incorrectly relate x and y, confirming that choice B is the only option that fully encompasses the solution set as depicted in the figure.

The shaded region in the figure above represents the solution set of which system of inequalities?

0 <= x <= 2, 0 <= y <= x + 2.

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