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 y< 2x+2/3 and y> 2x+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 + 2/3 is the region below the line y = 2x + 2/3; and 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.

Step 1: 6x-10=1; step 2: 6x=11