The shaded region in the following figure represents a solution set of

Step-by-step solution

To determine the inequalities representing the shaded region, analyze the boundary lines and the position of the shading relative to these lines. The boundaries include the lines x - y = 0 (or y = x ) and x + y = 0 (or y = -x ). The region lies below y = x , implying y 0 . Using a test point such as (2, 0) confirms this: 2 - 0 = 2 > 0 . It also lies above y = -x , so y > -x , leading to x + y > 0 . The test point (2, 0) again satisfies this: 2 + 0 = 2 > 0 . The inequalities are therefore x - y > 0 and x + y > 0 , w