Question

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?

Answer 1

Sample Response: There is no solution to the system in its original form. There are no points in common. If the signs are reversed, the system has an intersection with an infinite number of solutions.

Answer 2

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.