Use the image to answer the question.

Question

the grid shows the problems:
y>-1/3x
y<-1/3x-2

A Cartesian coordinate plane's axes range from negative 4 to 4, both by 1-unit increments. 2 dashed lines with arrows at both ends are plotted, and various regions of the graph are marked.

Select a true statement to describe the graphed system of inequalities.

(1 point)
Responses

The system has no solutions.
The system has no solutions.

The system has one solution.
The system has one solution.

The system has infinite solutions.
The system has infinite solutions.

The system has two solutions.

Answer 1

To determine the nature of the solutions for the given system of inequalities, we can analyze the inequalities and their graphical representations.

1. The first inequality, \( y > -\frac{1}{3}x \), represents the area above the dashed line corresponding to this equation.

2. The second inequality, \( y < -\frac{1}{3}x - 2 \), represents the area below the dashed line corresponding to this equation.

Considering that both lines are dashed, the regions described by the inequalities do not include the lines themselves but represent their respective half-planes.

To find the solution set for the system of inequalities, we need to look for the intersection of the two regions described by the inequalities. Since one inequality describes the area above a line and the other describes the area below a different line, there is a potential for overlap.

Conclusion: The graph of the system shows that there will be a region where both conditions are satisfied. Therefore, the system has infinite solutions, as there is an entire area (region) that meets both inequality conditions.

The correct answer is:

The system has infinite solutions.