Question

1. identify the system of inequalities that represents the constraints shown on this graph. view image description options: \\(\

$$\begin{cases} x \\geq -1 \\\\ x < 3 \\\\ y \\leq 3 \\\\ y > -2 \\end{cases}$$

\\); \\(\

$$\begin{cases} x > -1 \\\\ x \\geq 3 \\\\ y < 3 \\\\ y \\leq -2 \\end{cases}$$

\\); \\(\

$$\begin{cases} x \\leq -1 \\\\ x > 3 \\\\ y \\geq 3 \\\\ y < -2 \\end{cases}$$

\\); \\(\

$$\begin{cases} x < -1 \\\\ x \\leq 3 \\\\ y > 3 \\\\ y \\geq -2 \\end{cases}$$

\\)

Explanation:

Step1: Analyze vertical lines (x - constraints)

First, look at the vertical dashed and solid lines. The left vertical line (solid) suggests \( x \geq -1 \) (since solid line includes the boundary), and the right vertical dashed line suggests \( x < 3 \) (dashed line excludes the boundary).

Step2: Analyze horizontal lines (y - constraints)

The top horizontal solid line suggests \( y \leq 3 \) (solid line includes the boundary), and the bottom horizontal dashed line suggests \( y > -2 \) (dashed line excludes the boundary).

Step3: Match with options

Check each option. The first option has \( x \geq -1 \), \( x < 3 \), \( y \leq 3 \), \( y > -2 \), which matches the analyzed constraints. Other options have conflicting inequalities (e.g., second option has \( x \geq 3 \) which contradicts, third has \( x > 3 \) and wrong y, fourth has \( x < -1 \) and wrong y).

Answer:

\(

$$\begin{cases} x \geq -1 \\ x < 3 \\ y \leq 3 \\ y > -2 \end{cases}$$

\) (the first option in the list)