Answer:
The correct graph is the one where the shaded region is below the dashed line x + y = 12 and above the solid line y = x - 4.
Explanation:
To determine which graph represents the solution set of the system of inequalities, we need to analyze each inequality separately and then combine their solutions.
Inequality 1: x + y < 12
This inequality represents all points below the line x + y = 12. Since it's a strict inequality (less than), the line itself is not included, so it should be represented by a dashed line.
Inequality 2: y ≥ x - 4
This inequality represents all points above the line y = x - 4. Since it's a non-strict inequality (greater than or equal to), the line itself is included, so it should be represented by a solid line.
The solution set of the system of inequalities is the region where both inequalities are satisfied simultaneously. This means we need to find the area that is both below the dashed line x + y = 12 and above the solid line y = x - 4.
Based on this analysis, the correct graph is the one where the shaded region is below the dashed line x + y = 12 and above the solid line y = x - 4.