How will the solution of the system y>2x+2/3 and y<2x+1/3 change if the inequality sign on both inequalities is reversed to y2x+1/3?

Draw the two lines y = 2x + 2/3, and y = 2x + 1/3. They are parallel and the line y = 2x + 2/3 is located over the line y = 2x + 1/3.

The solution of the inequality y > 2x + 2/3 is the region above the line y = 2x + 2/3, and the solution of the inequality y < 2x + 1/3 is the region below the line 2x + 1/3, this means that there is no intersection and the system has no solution.

When the inequality sign of both inequalites is reversed, the solution of y 2x + 1/3 is the region above the line y = 2x + 1/3. That means that the solution of the system is the region between the two lines.

So, from not having solution the system changed to have solution.