Answer
Bboth equations are satisfied by the coordinates of point A, which means that the point lies in the healthy weight region.
Work Step by Step
The point A has coordinates $\left( 66,160 \right)$. So, in order to check whether this point lies in the healthy weight region or not, substitute the coordinates of point A for the x and y variables respectively in both the provided equations as shown below:
$\begin{align}
& 5.3x-y\ge 180 \\
& 5.3\left( 66 \right)-160\ge 180 \\
& 189.8\ge 180
\end{align}$
And the inequality holds.
Now, put the values in the second equation:
$\begin{align}
& 4.1x-y\le 140 \\
& 4.1\left( 66 \right)-160\le 140 \\
& 110.6\le 140
\end{align}$
Here also the inequality holds.
Thus, both equations are satisfied by the coordinates of point A, which means that the point lies in the healthy weight region.
