Math Problem Statement
What system of inequalities is shown by the graph?
Solution
The graph in the image appears to represent a system of inequalities. Here's how we can interpret it:
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The horizontal dashed red line at :
- Since the shading is below this line, the inequality is .
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The vertical dashed blue line at :
- Since the shading is to the left of this line, the inequality is .
The System of Inequalities
The system of inequalities described by the graph is:
y \leq 2 \\ x \leq -2 \end{cases}$$ Would you like a detailed explanation of how shading and boundaries correspond to inequalities? Here are some related questions for further exploration: 1. How do we distinguish between $$<$$ and $$\leq$$ in graphs of inequalities? 2. What happens to the shading when the inequality is $$>$$ instead of $$<$$? 3. How can we test a specific point to determine if it satisfies a system of inequalities? 4. What is the significance of dashed vs. solid lines in graphing inequalities? 5. How do graphs of inequalities change when you switch variables (e.g., $$y$$ and $$x$$)? **Tip:** Always test a point in the shaded region (e.g., $$(-3, 0)$$) to verify it satisfies all the inequalities!Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Graphing Inequalities
Coordinate Plane
Formulas
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Theorems
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Suitable Grade Level
Grades 7-9