Question

solving systems of linear inequalities
which system of linear inequalities is represented by the graph?
$y < x - 2$ and $y > x + 1$
$y \geq x - 2$ and $y \leq x + 1$
$y > x - 2$ and $y < x + 1$
$y \leq x - 2$ and $y \geq x + 1$

Explanation:

Step1: Analyze the blue line (dashed)

The blue line has a slope of 1 and y - intercept - 2, so its equation is \(y = x - 2\). Since the line is dashed, the inequality is strict (\(>\) or \(<\)). The shaded region above the blue line means \(y>x - 2\).

Step2: Analyze the red line (dashed)

The red line has a slope of 1 and y - intercept 1, so its equation is \(y=x + 1\). Since the line is dashed, the inequality is strict (\(>\) or \(<\)). The shaded region below the red line means \(y

Step3: Match with options

The system \(y>x - 2\) and \(y

Answer:

\(y > x - 2\) and \(y < x + 1\) (the third option in the list)