Question

In Problems 49 and 50, graph each system of inequalities by hand.

$\left\{\begin{array}{l}{x}^2+y^2\le 25\\ xy\le 4\end{array}\right.$

Short answer

The graph of$\left\{\begin{array}{l}{x}^2+y^2\le 25\\ xy\le 4\end{array}\right.$is

Step-by-step solution

Step 1. Given data 

The given system of inequality is

$\left\{\begin{array}{l}{x}^2+y^2\le 25\\ xy\le 4\end{array}\right.$

Step 2. Properties of the graph of the inequality    

Graph of$x^2+y^2\le 25$ will be a circle of center$(0,0)$

now test the origin point $(0,0)$for inequality$x^2+y^2\le 25$

$$\begin{gathered} x^2+y^2\le 25 \\ {0}^2+0^2\le 25 \\ 0<25 \end{gathered}$$

inequality satisfied so the origin will lie in the region of inequality

So the region inside the circle will be shaded

Step 3. Properties of the graph of the inequality    

Test the point $(0,0)$for inequality $xy\le 4$

$$\begin{gathered} xy\le 4 \\ 0\times 0\le 4 \\ 0<4 \end{gathered}$$

inequality satisfied so the origin will lie in the region of inequality$xy\le 4$

So the region toward origin from the graph ofrole="math" localid="1646962893657" $xy=4$ will be shaded

Step 4. graph of the system of inequality   

Graph of the system of inequality is