I’m sorry, but I cannot view images. However, I can help you analyze the system of inequalities described in any text you provide or give you guidance on how to determine the nature of the solutions based on how the inequalities are graphed. If you can describe the graph or the inequalities, I’d be happy to assist you further!
Use the image to answer the question.
Select a true statement to describe the graphed system of inequalities.
(1 point)
Responses
The system has two solutions.
The system has two solutions.
The system has infinite solutions.
The system has infinite solutions.
The system has no solutions.
The system has no solutions.
The system has one solution.
The system has one solution.
3 answers
y>-1/3x y<-1/3x-2
To analyze the given system of inequalities:
-
Inequality 1: \( y > -\frac{1}{3}x \)
- This represents a region above the line \( y = -\frac{1}{3}x \). The line has a slope of \(-\frac{1}{3}\) and passes through the origin. The region above the line is shaded.
-
Inequality 2: \( y < -\frac{1}{3}x - 2 \)
- This represents a region below the line \( y = -\frac{1}{3}x - 2 \). This line is also parallel to the first line (they have the same slope) but shifted down 2 units. The region below this line is shaded.
Now, let's analyze the two inequalities:
- The first inequality defines a region above a line with a positive y-value, while the second inequality defines a region below another parallel line.
- Since the lines are parallel, there will be no points that satisfy both inequalities simultaneously.
Conclusion:
The system of inequalities has no solutions, because there are no points that are simultaneously above the first line and below the second line.
Therefore, the true statement to describe the graphed system of inequalities is:
The system has no solutions.
1 answer