Chapter 1.8, Problem 21E

To determine

To graph: the region satisfying the given inequality.

Answer to Problem 21E

  

Explanation of Solution

Given information:

  $x\ge 0\text{ and }y\ge 0$

Calculation:

Since the inequality $x\ge 0$ has greater than or equal to sign $(\le )$ , solid line will be used to graph a line $x=0$ .

Put the test points $\left(1,1\right),\left(3,-3\right),\left(-2,2\right)$ and $\left(-4,-4\right)$ in the inequality and check the true test point as follows:

Test point $\left(x,y\right)$	Inequality, $x\ge 0$	True/False test point
$\left(1,1\right)$	$1\ge 0$	True
$\left(3,-3\right)$	$3\ge 0$	True
$\left(-2,2\right)$	$-2\ge 0$	False
$\left(-4,-4\right)$	$-4\ge 0$	False

Since the inequality $y\ge 0$ has greater than or equal to sign $(\le )$ , solid line will be used to graph a line $x=0$ .

Put the test points $\left(1,1\right),\left(3,-3\right),\left(-2,2\right)$ and $\left(-4,-4\right)$ in the inequality and check the true test point as follows:

Test point $\left(x,y\right)$	Inequality, $y\ge 0$	True/False test point
$\left(1,1\right)$	$1\ge 0$	True
$\left(-2,2\right)$	$2\ge 0$	True
$\left(3,-3\right)$	$-3\ge 0$	False
$\left(-4,-4\right)$	$-4\ge 0$	False

Thus, the shared true test point is $\left(1,1\right)$ .

The graph for the given inequality is shown below.