The correct answer is d. This choice shades the dark blue area correctly, showing the intersection of both inequalities.
Step 1: Graph the first inequality, y > x - 6.
Since we're dealing with an inequality, we'll use a dashed line for the boundary. We can start by graphing the equal part of the inequality, y = x - 6, which is a solid blue line. For y > x - 6, we shade the area above the blue line. This represents all the points where y is greater than x - 6.
Step 2: Graph the second inequality, 56 < x.
We're dealing with another inequality here, so we'll use a dashed line for the boundary. Graph the equal part of the inequality, x = 56, which is a vertical dashed green line. Since we want x values greater than 56, we shade the area to the right of the green line. This represents all the points where x is greater than 56.
Step 3: Find the intersection of the two shaded areas.
The solution to the system of inequalities is the area where the shading from both inequalities overlaps. This is the dark blue area in the graph.
Step 4: Check the answer choices.
Only answer choice d has its shading consistent with the dark blue area in the graph. Therefore, it's the correct answer.
Here's the breakdown of each answer choice:
a): This choice only shades the area above the y = x - 6 line, but it doesn't consider the x > 56 constraints. It's incorrect.
b): This choice shades the correct area for y > x - 6 but incorrectly shades the area to the left of the x = 56 line. It's incorrect.
c): This choice shades the correct area for x > 56 but incorrectly shades the area below the y = x - 6 line. It's incorrect.
d): This choice shades the dark blue area correctly, showing the intersection of both inequalities. It's the correct answer.