To solve the system of inequalities and determine which graph represents the solution set, let's analyze the given inequalities:
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Inequality: \( y \geq |x| \)
- This inequality represents the area above the V-shaped graph of \( y = |x| \). The vertex of the V is at the origin (0, 0), and the arms of the V extend outwards.
- Since it is greater than or equal to, the line itself is included in the solution set (solid line).
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Inequality: \( y \leq 12x \)
- This inequality represents the area below the straight line \( y = 12x \).
- The line has a steep slope because 12 is a large number, indicating it will rise quickly as x increases.
- Since it is less than or equal to, this line is also included in the solution set (solid line).
Finding the Intersection
The solution set is where the region above the V and the region below the line \( y = 12x \) overlap.
Determining the Correct Graph
You need to find a graph that:
- Shades the area above the V (which opens upward) for \( y \geq |x| \).
- Shades the area below the steep line for \( y \leq 12x \).
Given that I cannot see the images or graphs mentioned in your options, I recommend looking for:
- A shaded region where the top boundary is the V shape (the sides should go upwards from the origin).
- The bottom boundary should be a straight line that slopes steeply upwards.
Check each of your images for these criteria to identify which represents the solution set correctly. If there are specific details about the graphs you can share, I can provide more insight!
5 answers