4. \( \left\{\begin{array}{l}6 y=6 x+24 \\ -3 x+3 y=12\end{array}\right. \)

Let’s have some fun solving this system of equations! First, we can simplify the equations a bit. The first equation \(6y = 6x + 24\) can be simplified by dividing everything by 6, giving us \(y = x + 4\). Now, substitute \(y\) into the second equation \(-3x + 3y = 12\). Replacing \(y\), we have: \[ -3x + 3(x + 4) = 12. \] Now, combine like terms: \[ -3x + 3x + 12 = 12. \] This simplifies to \(12 = 12\), which means the equations represent the same line, indicating an infinite number of solutions! So any point of the form \((x, x + 4)\) is a solution to this system. For those learning to solve linear equations, remembering that two equations could represent the same line is a key concept!