find the graph of this system of linear inequalities. $\begin{cases}ygeq\frac{x}{3}\\y<-\frac{x}{2}+2end{case…

Explanation:

Step1: Analyze the first inequality

The inequality $y\geq\frac{x}{3}$ has a boundary - line $y = \frac{x}{3}$ with a slope of $\frac{1}{3}$ and a y - intercept of 0. Since it is $y\geq\frac{x}{3}$, the region above the line (including the line itself) is part of the solution set, and the line is solid.

Step2: Analyze the second inequality

The inequality $y<-\frac{x}{2}+2$ has a boundary - line $y =-\frac{x}{2}+2$ with a slope of $-\frac{1}{2}$ and a y - intercept of 2. Since it is $y<-\frac{x}{2}+2$, the region below the line is part of the solution set, and the line is dashed.

Step3: Find the intersection region

The solution of the system of inequalities is the region that satisfies both inequalities simultaneously. That is the region that is above the line $y=\frac{x}{3}$ and below the line $y =-\frac{x}{2}+2$.

Answer:

The second graph (the one where the region between the solid blue line $y=\frac{x}{3}$ and the dashed red line $y =-\frac{x}{2}+2$ is shaded) is the correct graph of the system of linear inequalities.