Chapter 6, Problem 21PT

To determine

To solve the below mentioned inequalities by graphing:

  $x+y\le 5$

And $y\ge x+2$

Explanation of Solution

Given information :

Given the two inequalities:

  $\begin{array}{l}x+y\le 5\\ y\ge x+2\end{array}$

Graph : The graph plotted below using the inequalities:

  $\begin{array}{l}x+y\le 5\\ y\ge x+2\end{array}$

  

Equation $x+y\le 5$ is represented by light blue area in above graph.

And $y\ge x+2$ is represented by light green area in above graph.

Interpretation : From the above graph, we see that $x+y\le 5$ is the bottom area of line $x+y=5$ (including line $x+y=5$ ) which has been represented in light blue green. And we see that $y\ge x+2$ is the above area of the line $y=x+2$ ( including the value of $y=x+2$ ) which has been represented in the light green area.

So, final solution is common color area which is in dark green color. It covers the area bottom to $x+y=5$ and above to $y=x+2$ including the points on lines of common color and including points of intersection of the lines.