Final answer:
To answer the question, draw a rectangle by sketching vertical lines at x=5 and x=-5, and horizontal lines at y=3 and y=-3, and shade the interior of this rectangle to represent all points where |x|<5 and |y|<3.
Step-by-step explanation:
The question asks to sketch and shade the region in the xy-plane defined by the inequalities |x|<5 and |y|<3. This means we are looking for the set of all points (x, y) where the absolute value of x is less than 5, and the absolute value of y is less than 3.
To sketch this region, start by drawing two vertical lines at x = 5 and x = -5, and two horizontal lines at y = 3 and y = -3. The region of interest will be the rectangle formed by these four lines, not including the borders because the inequalities are strict (not less than or equal to). Finally, shade the rectangular region to indicate all the points that satisfy both inequalities simultaneously.