Question

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

$\left\{\begin{array}{l}{x}^2+y^2\le 16\\ x+y\ge 2\end{array}\right.$

Short answer

The graph of $\left\{\begin{array}{l}{x}^2+y^2\le 16\\ x+y\ge 2\end{array}\right.$is

Step-by-step solution

Step 1. Given data 

The given system of inequality is

$\left\{\begin{array}{l}{x}^2+y^2\le 16\\ x+y\ge 2\end{array}\right.$

Step 2. Properties of the graph of the inequality    

Graph of $x^2+y^2=16$will be a circle of center$(0,0)$

now test the origin point $(0,0)$for inequality $x^2+y^2\le 16$

$$\begin{gathered} x^2+y^2\le 16 \\ {0}^2+0^2\le 16 \\ 0<16 \end{gathered}$$

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    

Graph of $x+y=2$will be a line

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

$$\begin{gathered} x+y\ge 2 \\ 0+0\ge 2 \\ 0<2 \end{gathered}$$

inequality does not satisfy so the origin will not lie in the region of inequality

So the region above from the line will be shaded

Step 4. graph of the system of inequality   

The graph of the system of inequality is