Question

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

Explanation:

Step1: Analyze the upper boundary line

The upper line has a y-intercept of 1 and slope 1, so its equation is $y = x + 1$. The shaded region is below this line, and the line is solid, so the inequality is $y \leq x + 1$.

Step2: Analyze the lower boundary line

The lower line has a y-intercept of -2 and slope 1, so its equation is $y = x - 2$. The shaded region is above this line, and the line is solid, so the inequality is $y \geq x - 2$.

Step3: Match to the options

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

Answer:

$y \geq x - 2$ and $y \leq x + 1$ (first option)