Use the Systems of Inequalities graphed below to answer the questions. What is the inequality symbol of the green line? What is the inequality symbol of the purple line? Is the point (-3, -5) a solution to the system of inequalities? Is the point (1, 6) a solution to the system of inequalities?

1 answer

To answer your questions, I would need a visual representation of the graphs or specific descriptions of the lines and shading. However, I can offer some guidelines for how you can determine the inequality symbols and solutions to the inequalities based on typical characteristics of a graph of systems of inequalities.

  1. Inequality Symbol of the Green Line:

    • If the green line is a solid line, the inequality is either ≤ (less than or equal to) or ≥ (greater than or equal to).
    • If the green line is a dashed line, the inequality is either < (less than) or > (greater than).
  2. Inequality Symbol of the Purple Line:

    • Similar to the green line, if the purple line is solid, then it is ≤ or ≥.
    • If the purple line is dashed, then it is < or >.
  3. Checking Points Against Inequalities:

    • To determine if a point is a solution to the system, substitute the coordinates of each point into the inequalities represented by the lines and check if they hold true.
    • For instance, if the inequalities are:
      • Green line: \(y < mx + b\) (example of a dashed line)
      • Purple line: \(y \leq mx + b\) (example of a solid line)
    • You would plug in (-3, -5) and (1, 6) into both inequalities.
  4. Is the Point (-3, -5) a Solution?:

    • Substitute x = -3 and y = -5 into each inequality to see if both inequalities are satisfied.
  5. Is the Point (1, 6) a Solution?:

    • Similarly, substitute x = 1 and y = 6 into the inequalities to see if both are satisfied.

Without the specific graph or equations, I can only provide this general guidance. If you can share more details about the lines or inequalities, I could give more precise answers.