1. **State the problem:** We need to determine which system of inequalities matches the described graph. 2. **Analyze the given lines:** - Line 1: crosses y-axis at 4, slope = -2, inequality is $y \leq -2x + 4$ (shaded above and to the left). - Line 2: crosses y-axis at -5, slope = 1 (positive), inequality is $y \geq x - 5$ (shaded below and to the right). 3. **Check each system:** - Option 1: $y \leq -2x + 4$ AND $y \geq x - 5$ matches the description. - Option 2: $y \geq -2x + 4$ AND $y \leq x - 5$ reverses shading. - Option 3 and 4 have different slopes and intercepts. 4. **Conclusion:** The system matching the graph is: $$y \leq -2x + 4 \quad \text{AND} \quad y \geq x - 5$$ This matches the shaded region in the top-left where $y$ is less than or equal to the first line and greater than or equal to the second line. Final answer: $y \leq -2x + 4$ AND $y \geq x - 5$