Chapter 3.3, Problem 24PPSE

Solution

To solve: The system of inequality using the graphing method $\left(\begin{array}{l}y>x-2\\ y\ge \left|x-2\right|\end{array}\right.$ .

Given information:

The given system of inequalities is $\left(\begin{array}{l}y>x-2\\ y\ge \left|x-2\right|\end{array}\right.$ .

Concept used:

Graph each inequality and then overlapping region is the solution of the system.

Plot the graph:

The graph of the inequality $y>x-2$ is given below.

  

The graph of the inequality $y>\left|2x-1\right|$ is given below:

  

The graph of the system of inequalities $\left(\begin{array}{l}y>x-2\\ y\ge \left|x-2\right|\end{array}\right.$ is given below:

  

Now to check any two point from the overlapping region and check the solution region is true or not.

Take the point $\left(2,3\right)$

For $\left(2,3\right)$ check $y>x-2\text{and}\text{y}\ge \left|x-2\right|$ :

  $3>0,3\ge 0$ ,both inequalities are true to the point $\left(2,3\right)$ .

So the overlapping region is the solution of the system of given inequalities.