Math Problem Statement
Graph the solution of the following system.
x minus yx−y
greater than or equals≥
minus−66
negative 3 x minus y−3x−y
less than or equals≤
55
Question content area bottom left
Part 1
Use the graphing tool to graph the system.
Solution
Here is the graph of the solution region for the system of inequalities. The blue area represents the overlap where both inequalities are satisfied.
Would you like further details on interpreting this graph or have any other questions?
Here are some related questions to deepen your understanding:
- How do you determine which region to shade for each inequality?
- What changes if the inequalities are strict ( or ) rather than inclusive ( or )?
- How would you find specific points that lie within the solution region?
- How do you verify if a given point satisfies both inequalities?
- What happens to the solution region if we change one inequality to its opposite?
Tip: When graphing inequalities, always check whether the boundary line itself is part of the solution by looking at the inequality type ( or ).
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Math Problem Analysis
Mathematical Concepts
Algebra
Inequalities
Graphing Systems of Inequalities
Formulas
Slope-intercept form of a line: y = mx + b
Converting inequalities to boundary lines for graphing
Theorems
Linear Inequalities
Solution Region of Systems of Inequalities
Suitable Grade Level
Grades 9-10
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