Case Study

Does this system have a solution? Explain your reasoning based on the graph.

Case context: A system of two linear inequalities is graphed. The boundary lines are parallel and the shaded regions face away from each other.

Question: Does this system have a solution? Explain your reasoning based on the graph.

Sample answer: No, the system has no solution because the shaded regions do not overlap.

Key points:

  • The system has no solution.
  • The shaded regions do not overlap.

Rubric: A correct response states that there is no solution and explains that the lack of overlapping shaded regions means there are no points that satisfy both inequalities.

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Updated 2026-06-16

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