which system of linear inequalities is represented by the graph?\no y≥x - 2 and x - 2y < 4\no y≥x + 2 and x…

Answer:

A. $y\geq x - 2$ and $x-2y<4$

Explanation:

Step1: Analyze the first line

The line with slope 1 and y - intercept - 2 has a solid line, so the inequality is $y\geq x - 2$.

Step2: Analyze the second line

Rewrite $x-2y<4$ as $y>\frac{1}{2}x - 2$. The other line has a dashed line and a slope of $\frac{1}{2}$ and y - intercept - 2. Also, for $x-2y<4$, we can test a point in the shaded region. For example, $(0,0)$: $0-2\times0 = 0<4$, which is consistent with the shaded region.

Step3: Check other options

For option B, the first inequality $y\geq x + 2$ has a y - intercept of 2 which is wrong. For option C, the first inequality is correct but the second one $x + 2y<4$ (or $y<-\frac{1}{2}x+2$) has a wrong slope for the second line. For option D, the second inequality $x + 2y<-4$ (or $y<-\frac{1}{2}x - 2$) has a wrong y - intercept and the wrong shaded region for the second line.