3. \( \left\{\begin{array}{l}-3 x+y=5 \\ 6 x-2 y=9\end{array}\right. \)

To solve the system of equations, we can use substitution or elimination. First, let's transform the second equation into a simpler form. The second equation can be rewritten as \( 3x - y = \frac{9}{2} \). Now we have: 1. \(-3x + y = 5\) 2. \(3x - y = \frac{9}{2}\) Adding these two equations can eliminate \(y\): \[ (-3x + y) + (3x - y) = 5 + \frac{9}{2} \] This simplifies to \(0 = 5 + 4.5\), which leads to a contradiction (0 ≠ 9.5), indicating that these lines are parallel and there is no solution to this system of equations. So, this means the system has no intersection points—no values for \(x\) and \(y\) that satisfy both equations simultaneously!