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

Question

−12x+y≥−1

y<2x

Use the image to answer the question.

(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.

Answer 1

To determine which graph represents the solution set of the given system of inequalities, we need to analyze each inequality:

1. The first inequality is \(-12x + y \geq -1\), which can be rewritten as: \[ y \geq 12x - 1 \] This represents a line with a slope of 12 and a y-intercept of -1. The region above this line is included in the solution set (the line itself is included due to the "greater than or equal to" sign).

2. The second inequality is \(y < 2x\). This represents a line with a slope of 2, and since it's a "less than" inequality, we will shade the region below this line (the line itself is not included).

To find the correct graph, look for the following characteristics:

• The area above the line \(y = 12x - 1\).
• The area below the line \(y = 2x\).

Once you identify these regions on the graph, the solution set will be the shaded area that is both above the line \(y = 12x - 1\) and below the line \(y = 2x\).

If the graph options you mentioned are images, you would compare the shadings and the lines' positions to determine which one correctly represents this situation.