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:

  1. How do you determine which region to shade for each inequality?
  2. What changes if the inequalities are strict (>> or <<) rather than inclusive (\geq or \leq)?
  3. How would you find specific points that lie within the solution region?
  4. How do you verify if a given point satisfies both inequalities?
  5. 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 (\geq 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