which system of inequalities has a solution set that is a line?\n$\begin{cases}x + ygeq3\\x +…

Explanation:

Step1: Analyze first - system

The system $\begin{cases}x + y\geq3\x + y\leq3\end{cases}$ means that $x + y$ must be both greater than or equal to 3 and less than or equal to 3. The only way for this to be true is when $x + y=3$. This is the equation of a line.

Step2: Analyze second - system

For the system $\begin{cases}x + y\geq - 3\x + y\leq3\end{cases}$, the solution - set is the region between the lines $x + y=-3$ and $x + y = 3$, which is a band - like region, not a line.

Step3: Analyze third - system

The system $\begin{cases}x + y>3\x + y<3\end{cases}$ has no solution because $x + y$ cannot be simultaneously greater than 3 and less than 3.

Step4: Analyze fourth - system

The system $\begin{cases}x + y>-3\x + y<3\end{cases}$ represents the region between the lines $x + y=-3$ and $x + y = 3$ (excluding the lines themselves), which is a band - like region, not a line.

Answer:

$\begin{cases}x + y\geq3\x + y\leq3\end{cases}$