Chapter 6.6, Problem 24PPE

To determine

To write: a system of inequalities represented by given graph.

Answer to Problem 24PPE

  $\begin{array}{l}3x+2y<6\\ x<1\end{array}$

Explanation of Solution

Given information: a figure is given as follows-

  

Since vertical dotted line is parallel to y-axis and it passes through (1, 0) so its equation is given by $x=1$ .

This divides the plane into two region and any point in the shaded region is satisfies $x<1$ , so one of the inequality which describes the shaded region is $x<1$

Another dotted line passes through the points (2, 0) and (0, 3). So its equation is given by

  $\begin{array}{l}\frac{y-0}{x-2}=\frac{3-0}{0-2}\\ \Rightarrow \frac{y}{x-2}=\frac{3}{-2}\\ \Rightarrow -2y=3x-6\\ \Rightarrow 3x+2y=6\end{array}$

The shaded region satisfies the $3x+2y<6$ , so other inequality which describes the shaded region is $3x+2y<6$ .