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

To solve the system of equations, let’s start with the first equation: \( -3x + y = 9 \). We can rearrange it as \( y = 3x + 9 \). Now, substitute \( y \) in the second equation: \( -3x + 2(3x + 9) = 9 \). Simplifying gives us \( -3x + 6x + 18 = 9 \) which leads to \( 3x + 18 = 9 \). Solving for \( x \) gives \( 3x = -9 \) or \( x = -3 \). Plugging \( x \) back in to find \( y \): \( y = 3(-3) + 9 = 0 \). Thus, the solution is \( (x, y) = (-3, 0) \). Now, check if these values satisfy the original equations as an essential step to confirm correctness. Substitute \( x = -3 \) and \( y = 0 \) back into both equations to ensure both hold true. If they do, you've not only found an answer but also practiced a solid method for solving systems of equations!