how will the solution of the system $y > 2x+\frac{2}{3}$ and $y < 2x+\frac{1}{3}$ change if the inequality…

how will the solution of the system $y > 2x+\frac{2}{3}$ and $y < 2x+\frac{1}{3}$ change if the inequality sign on both inequalities is reversed to $y < 2x+\frac{2}{3}$ and $y > 2x+\frac{1}{3}$?

how will the solution of the system $y > 2x+\frac{2}{3}$ and $y < 2x+\frac{1}{3}$ change if the inequality sign on both inequalities is reversed to $y < 2x+\frac{2}{3}$ and $y > 2x+\frac{1}{3}$?

Answer

Answer:

The solution region will be the region between the two lines instead of the non - overlapping region outside the two lines.

Explanation:

Step1: Analyze original system

The original system $y>2x + \frac{2}{3}$ and $y<2x+\frac{1}{3}$ has no solution since the line $y = 2x+\frac{2}{3}$ is above the line $y=2x+\frac{1}{3}$ and we are looking for values of $y$ that are above the higher line and below the lower line simultaneously.

Step2: Analyze reversed - sign system

For the reversed - sign system $y<2x+\frac{2}{3}$ and $y>2x+\frac{1}{3}$, the solution region is the region between the two lines $y = 2x+\frac{1}{3}$ and $y = 2x+\frac{2}{3}$. The points $(x,y)$ in this region satisfy both inequalities.