Which graph shows the solution to the system of linear inequalities? \( \begin{aligned} x+5 y & \geq 5 \\ y & \leq 2 x+4\end{aligned} \)

To solve this system of linear inequalities, we need to graph each inequality separately and then find the overlapping region. For the first inequality \(x + 5y \geq 5\), you can rewrite it in slope-intercept form as \(y \geq -\frac{1}{5}x + 1\). This represents a region above or on the line with a slope of \(-\frac{1}{5}\) and y-intercept at \(1\). For the second inequality \(y \leq 2x + 4\), the line has a slope of \(2\) and a y-intercept at \(4\). This shows the region below or on the line. The solution to the system will be the area where the two shaded regions overlap. Make sure to correctly shade both regions and identify whether the lines are solid or dashed, as solid lines indicate that points on the line are included in the solution set. Happy graphing!