Question

Which of the following is the solution to the following systems of inequalities? (picture included)

Answer 1

Answer:

  C.  (see the attachment)

Step-by-step explanation:

Both inequalities include the "or equal to" case, so both boundary lines will be solid. That excludes choices A and D.

The first inequality is plotted the same way in all graphs, so we must look at the second inequality. The relationship of y and the comparison symbol is ...

  -y ≥ (something)

If we multiply by -1, we get ...

  y ≤ (something else)

This means the solution space will be on or below (less than or equal to) the boundary line. This is the shaded area in graph C. (Graph B shows shading above the line.)

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Further comment

Since the boundary for the second inequality is fairly steep, "above" and "below" the line can be difficult to see. Rather, you can consider the relationship of x to the comparison symbol. For the second inequality, that is ...

  x ≥ (something)

indicating the solution space is on or to the right of the boundary line.