Final answer:
Reversing the inequality signs in the system y > 2x + 2/3 and y < 2x + 1/3 to y < 2x + 2/3 and y > 2x + 1/3 creates an impossible situation where no points satisfy both conditions, resulting in no solution for the system.
Step-by-step explanation:
Reversing the signs in the system of inequalities from y > 2x + 2/3 and y < 2x + 1/3 to y < 2x + 2/3 and y > 2x + 1/3 results in a change to the solution set. Initially, the solution was the region between the two lines, neither including them because both inequalities were strict. Now, by reversing the inequality signs, we are looking for a solution set that does not lie between these two lines. Since we can't have a value of y that is simultaneously less than 2x + 2/3 and greater than 2x + 1/3, the new system of inequalities actually represents an impossible situation, and there are no points that satisfy both conditions simultaneously.