#### Answer

Both equations are satisfied by the coordinates of point B, which means that the provided point lies in the healthy weight region.

#### Work Step by Step

The point B has coordinates $\left( 76,220 \right)$. So, in order to check whether this point lies in the healthy weight region or not, substitute the coordinates of point B for x and y variables respectively in both the provided equations as shown below:
Put the values in the first equation as given below:
$\begin{align}
& 5.3x-y\ge 180 \\
& 5.3\left( 76 \right)-220\ge 180 \\
& 182.8\ge 180
\end{align}$
And the inequality holds.
Now, put the values in the second equation as given below:
$\begin{align}
& 4.1\left( x \right)-y\le 140 \\
& 4.1\left( 76 \right)-220\le 140 \\
& 91.6\le 140
\end{align}$
Here also the inequality holds.
Thus, both equations are satisfied by the coordinates of point B, which means that the provided point lies in the healthy weight region.