Question

How will the solution of the system change if the inequality sign on both inequalities

Answer 1

Answer:

Shown below

Step-by-step explanation:

The first system of inequality is the following:

$\left\{ \begin{array}{c}y>2x+\frac{2}{3}\\y$

To find the solution here, let's take one point, say, $(0,0)$ and let's taste this point into both inequalities, so:

FIRST CASE:

First inequality:

$y>2x+\frac{2}{3} \\ \\ 0>2(0)+\frac{2}{3} \\ \\ 0>\frac{2}{3} \ False!$

The region is not the one where the point $(0,0)$ lies

Second inequality:

$y$

The region is the one where the point $(0,0)$ lies

So the solution in this first case has been plotted in the first figure. As you can see, there is no any solution there

SECOND CASE:

First inequality:

$y$

The region is the one where the point $(0,0)$ lies

Second inequality:

$y>2x+\frac{1}{3} \\ \\ 0>2(0)+\frac{1}{3} \\ \\ 0>\frac{1}{3} \ True!$

The region is not the one where the point $(0,0)$ lies

So the solution in this first case has been plotted in the second figure. As you can see, there is a solution there.

CONCLUSION: Notice that when reversing the signs on both inequalities the solution in the second case is the part of the plane where the first case didn't find shaded region.