which system of linear inequalities is represented by the graph?\n$ygeq\frac{1}{3}x + 3$ and $3x…

Explanation:

Step1: Analyze the first line

The first line has a y - intercept of 3 and a slope of $\frac{1}{3}$. The shaded region is above the line, so the inequality is $y\geq\frac{1}{3}x + 3$.

Step2: Analyze the second line

Rewrite the general form of a line $Ax+By = C$ to slope - intercept form $y=mx + b$. For the second line, we can check the options by rewriting them in slope - intercept form. For $3x - y>2$, we can rewrite it as $y<3x - 2$. For $3x + y>2$, we rewrite it as $y>-3x + 2$. For $2x - y>2$, we rewrite it as $y<2x - 2$. The second line has a negative slope. The line with a negative slope in the graph has a y - intercept of 2 and a slope of - 3. The inequality for the second line with the shaded region above it (since the line is dashed) is $3x + y>2$.

Answer:

$y\geq\frac{1}{3}x + 3$ and $3x + y>2$ (the third option)