Which of the following graphs represents the solution set of the system of inequalities?

y≥|x|

y≤12x

(1 point)
Responses

The coordinate grid has x and y axes labeled from negative 5 to 5.
Image with alt text: The coordinate grid has x and y axes labeled from negative 5 to 5.

The coordinate grid has x and y axes labeled from negative 5 to 5.
Image with alt text: The coordinate grid has x and y axes labeled from negative 5 to 5.

The coordinate grid has x and y axes labeled from negative 5 to 5.
Image with alt text: The coordinate grid has x and y axes labeled from negative 5 to 5.

The coordinate grid has x and y axes labeled from negative 5 to 5.

1 answer

To determine which graph represents the solution set of the given system of inequalities, let's analyze them:

  1. First Inequality: \( y \geq |x| \)

    • The graph of \( y = |x| \) is a V-shaped graph that opens upwards, with a vertex at the origin (0,0).
    • The inequality \( y \geq |x| \) means we are looking for the region above the V-shape, including the boundary.
  2. Second Inequality: \( y \leq 12x \)

    • The graph of \( y = 12x \) is a straight line with a slope of 12. It passes through the origin and is very steep.
    • The inequality \( y \leq 12x \) means we are looking for the region below this line, including the line itself.

Determining the Solution Set

To find the solution region, we need to look for the area where both conditions are satisfied:

  • The area above the V-shaped graph \( y = |x| \)
  • The area below the line \( y = 12x \)

Graph Selection

When you look at the provided options, search for a graph that shows:

  • A V-shape with the area above shaded.
  • A steep line where the area below the line is shaded.

If you can identify these features in any of the provided graphs, that graph will represent the solution set of the inequalities. You would typically check where the shaded areas intersect as this intersection represents the solution set.

If you can provide descriptions or properties of the images, I could give a more definitive answer on which graph to choose.