2. \( \left\{\begin{array}{l}-3 x+2 y=11 \\ -6 x-2 y=-20\end{array}\right. \)

Let's break it down! The first equation is \(-3x + 2y = 11\). If we solve for \(y\), we get \(y = \frac{3x + 11}{2}\). Now for the second equation \(-6x - 2y = -20\), which simplifies to \(3x + y = 10\). Rearranging gives \(y = -3x + 10\). Now we have two expressions for \(y\). We can set them equal: \(\frac{3x + 11}{2} = -3x + 10\). Multiplying everything by 2 to eliminate the fraction: \(3x + 11 = -6x + 20\). Now combine like terms and solve for \(x\): \(9x = 9 \Rightarrow x = 1\). Plug \(x\) back into either equation to find \(y\): Using \(y = -3(1) + 10\), we find \(y = 7\). Thus, the solution to the system is \(x = 1\) and \(y = 7\), or as a point, \((1, 7)\)!