y> or equal to -1, y<-2

Which description is true about the graphed system of inequalities
The system had no solutions
The system has one solution
The system has two solutions
The system has infinite solutions

1 answer

To analyze the system of inequalities given:

  1. \( y \geq -1 \)
  2. \( y < -2 \)

Let's interpret these inequalities:

  • The first inequality \( y \geq -1 \) represents all values of \( y \) that are greater than or equal to \(-1\). This forms a region that includes the line \( y = -1 \) and all points above it.

  • The second inequality \( y < -2 \) represents all values of \( y \) that are less than \(-2\). This forms a region below the line \( y = -2 \).

Now, let's visualize these regions on a graph:

  • The area representing \( y \geq -1 \) is above the line \( y = -1\).
  • The area representing \( y < -2 \) is below the line \( y = -2\).

These two regions do not overlap since any value of \( y \) that is greater than or equal to \(-1\) cannot also be less than \(-2\).

Therefore, there are no \( y \) values that satisfy both inequalities at the same time.

Based on this analysis, the correct description of the graphed system of inequalities is:

The system had no solutions.