Question

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

Answer 1

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.**