1. **State the problem:** Determine if the point $(-2, -3)$ satisfies the system of inequalities represented by the two lines and their shaded regions. 2. **Identify the inequalities from the graph description:** - Green line: passes near $(-5,4)$ and $(5,-1)$ with shading above the line. - Blue line: passes near $(1,5)$ and $(5,-5)$ with shading below the line. 3. **Find the equations of the lines:** - Green line slope: $$m = \frac{-1 - 4}{5 - (-5)} = \frac{-5}{10} = -\frac{1}{2}$$ - Green line equation using point-slope form with point $(-5,4)$: $$y - 4 = -\frac{1}{2}(x + 5)$$ $$y = -\frac{1}{2}x - \frac{5}{2} + 4 = -\frac{1}{2}x + \frac{3}{2}$$ - Blue line slope: $$m = \frac{-5 - 5}{5 - 1} = \frac{-10}{4} = -\frac{5}{2}$$ - Blue line equation using point-slope form with point $(1,5)$: $$y - 5 = -\frac{5}{2}(x - 1)$$ $$y = -\frac{5}{2}x + \frac{5}{2} + 5 = -\frac{5}{2}x + \frac{15}{2}$$ 4. **Write inequalities based on shading:** - Green line shading above: $$y \geq -\frac{1}{2}x + \frac{3}{2}$$ - Blue line shading below: $$y \leq -\frac{5}{2}x + \frac{15}{2}$$ 5. **Check if $(-2, -3)$ satisfies both inequalities:** - For green line: $$-3 \stackrel{?}{\geq} -\frac{1}{2}(-2) + \frac{3}{2} = 1 + 1.5 = 2.5$$ $$-3 \geq 2.5 \text{ is false}$$ - For blue line: $$-3 \stackrel{?}{\leq} -\frac{5}{2}(-2) + \frac{15}{2} = 5 + 7.5 = 12.5$$ $$-3 \leq 12.5 \text{ is true}$$ 6. **Conclusion:** The point $(-2, -3)$ does not satisfy the green line inequality (shading above), so it is not a solution to the system. **Final answer:** No, $(-2, -3)$ is not a solution of the graphed system of inequalities.