Question

1. \

$$\begin{cases} y \\leq -\\frac{3}{5}x \\\\ y > -x - 4 \\end{cases}$$

Explanation:

Step1: Graph boundary $y=-\frac{3}{5}x$

This is a solid line (since $\leq$ includes equality) with slope $-\frac{3}{5}$ and y-intercept $(0,0)$. Plot points: when $x=5$, $y=-3$; when $x=-5$, $y=3$. Draw a solid line through these points.
Shade the region below this line (because $y \leq -\frac{3}{5}x$).

Step2: Graph boundary $y=-x-4$

This is a dashed line (since $>$ does not include equality) with slope $-1$ and y-intercept $(0,-4)$. Plot points: when $x=-4$, $y=0$; when $x=0$, $y=-4$. Draw a dashed line through these points.
Shade the region above this line (because $y > -x-4$).

Step3: Identify overlapping region

The solution is the area where the two shaded regions overlap.

Answer:

The solution is the overlapping shaded region: below the solid line $y=-\frac{3}{5}x$ and above the dashed line $y=-x-4$.
(On the provided grid, this overlapping area covers points such as $(0,0)$, $(-5,1)$, and $(5,-4)$ as valid points in the solution set.)