Final Answer:
The shaded region on the grid represents the solution to the system of inequalities x ≤ 5, y ≥ 3, and y ≤ x.
Step-by-step explanation:
To determine the shaded region, let's address each inequality individually. The inequality x ≤ 5 denotes a vertical line passing through x = 5 on the grid, including all points to the left of this line. Next, y ≥ 3 represents a horizontal line at y = 3, encompassing all points above this line.
The inequality y ≤ x signifies a boundary where y equals x, forming a line at a 45-degree angle passing through the origin (0,0) and extending infinitely.
The region satisfying x ≤ 5 is to the left of the vertical line at x = 5, while y ≥ 3 encompasses the area above the horizontal line at y = 3. Additionally, y ≤ x forms a boundary where the values of y are less than or equal to their corresponding x values.
Combining these constraints, the shaded region where all three inequalities hold true lies in the area where x is less than or equal to 5, y is greater than or equal to 3, and y is less than or equal to x.
This shaded region forms a triangular area bounded by the lines x = 5, y = 3, and the line y = x. This graphical representation visually displays the solution to the system of inequalities given.