Chapter 6.6, Problem 21PPE

To determine

To solve: the given system of inequalities using graphing.

Explanation of Solution

Given information:

The given system of inequalities is

  $\begin{array}{l}6x-5y<15\\ x+2y\ge 7\end{array}$

Calculation:

Find the intercepts

Consider the equation $6x-5y=15$

  $\begin{array}{l}y=0\Rightarrow x=2.5\\ x=0\Rightarrow y=-3\end{array}$

Consider the equation $x+2y=7$

  $\begin{array}{l}y=0\Rightarrow x=7\\ x=0\Rightarrow y=3.5\end{array}$

Draw the dashed line passing through the points $(2.5,0)\&(0,-3)$ and shade below the line.

Draw the dashed line passing through the points $(7,0)\&(0,3.5)$ and shade above the line.

Graph:

The graph of given system of inequalities is shown below.

  

Hence, the common shaded region is the solution of the given system.