Question

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

Explanation:

Step1: Identify line equations

The two lines have slopes of 1. The upper line has a y-intercept of 1, so its equation is $y = x + 1$. The lower line has a y-intercept of -2, so its equation is $y = x - 2$.

Step2: Analyze upper inequality

The shaded region is below the solid line $y = x + 1$, so the inequality is $y \leq x + 1$.

Step3: Analyze lower inequality

The shaded region is above the solid line $y = x - 2$, so the inequality is $y \geq x - 2$.

Step4: Match to options

Combine the two inequalities: $y \geq x - 2$ and $y \leq x + 1$.

Answer:

$y \geq x - 2$ and $y \leq x + 1$