Final answer:
The shaded region defined by the inequalities y ≥ x and y ≥ -x is located in Quadrants I and II of the coordinate plane, as these are the only quadrants that satisfy both conditions simultaneously.
Step-by-step explanation:
The student is asking about the location of a shaded region in a system of inequalities on the coordinate plane. In this system, the inequalities are y ≥ x (which represents all the points above and on the line y = x) and y ≥ -x (which represents all the points above and on the line y = -x). In terms of quadrants, this shaded region would be found where both inequalities are satisfied. The inequality y ≥ x includes Quadrant I, where both x and y are positive, and Quadrant II, where x is negative and y is positive. Meanwhile, the inequality y ≥ -x includes Quadrant I, where x and y are both positive, and Quadrant IV, where x is positive and y is negative. The region where both inequalities are true is the overlap between the regions defined by each inequality, which would be Quadrant I, as it is the only quadrant satisfying both conditions. Therefore, the answer to the question: In which quadrants of the coordinate plane is the shaded region of the system located, where y is greater than or equal to x and y is greater than or equal to -x? is b. Quadrants I and II.