To determine which graph represents the solution set of the given system of inequalities, we need to analyze each inequality separately.
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Inequality 1: \( -12x + y \geq -1 \)
Rearranging this gives us: \[ y \geq 12x - 1 \] The graph of the line \( y = 12x - 1 \) has a slope of 12 and a y-intercept of -1. Since the inequality is "greater than or equal to," we will shade above the line (including the line itself, since it is "greater than or equal").
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Inequality 2: \( y < 2x \)
This represents the area below the line \( y = 2x \), and since it is "less than," we will shade below this line (not including the line itself).
To find the solution set for the system, we look for the region that satisfies both inequalities: the area that is above the line \( y = 12x - 1 \) and below the line \( y = 2x \).
Next, you would refer to the provided graph images to see which one contains the appropriate shaded region based on the inequalities described above.
Since I can't see the images, I suggest looking for a graph where:
- The area above the line \( y = 12x - 1 \) is shaded,
- The area below the line \( y = 2x \) is shaded,
- The overlapping shaded region is the solution set for the system.
Make sure the line for \( y = 12x - 1 \) is solid, and the line for \( y = 2x \) is dashed. Once you've identified the graph that meets these criteria, that will be your answer.