To determine the nature of the solutions for the given system of inequalities, we can analyze the inequalities and their graphical representations.
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The first inequality, \( y > -\frac{1}{3}x \), represents the area above the dashed line corresponding to this equation.
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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.