To find the system of inequalities that represents the shaded region, we need to identify each boundary line, determine its equation, and then establish the correct inequality based on the shaded area

To find the system of inequalities that represents the shaded region, we need to identify each boundary line, determine its equation, and then establish the correct inequality based on the shaded area.

There are four boundary lines for the shaded region:

1. The dashed line (upper boundary):

• This line passes through the points $(-4, 0)$ and $(0, 2)$.
• Calculate the slope $m$: $m = \frac{2 - 0}{0 - (-4)} = \frac{2}{4} = \frac{1}{2}$.
• Using the point-slope form $y - y_1 = m(x - x_1)$ with $(0, 2)$: $y - 2 = \frac