Chapter 12.2, Problem 51E

To determine

To graph:

System $xy\ge 2$ and $x-3y=2$

Explanation of Solution

Given information:

Given system: $xy\ge 2$ and $x-3y=2$

Graph:

Interpretation:

Consider the given system of inequalities,

  $\begin{array}{l}xy\ge 2\\ y\ge \frac{2}{x}\end{array}$

And

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

Table given below represents above equations:

$x$	$y=2/x$	$y=\frac{-2+x}{3}$
$-5$	$0.4$	$-2.33$
$-4$	$-0.5$	$-2$
$-3$	$-0.6667$	$-1.66667$
$-2$	$-1$	$-1.3333$
$-1$	$-2$	$-1$
$0$	undefined	$-0.6667$
$1$	$2$	$-0.333333$
$2$	$1$	$0$
$3$	$0.66667$	$0.333333$
$4$	$0.5$	$0.66667$
$5$	$0.4$	$1$