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

Solve the system of equations \( 6y=6x+24;-3x+3y=12 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}6y=6x+24\\-3x+3y=12\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=y-4\\-3x+3y=12\end{array}\right.\) - step2: Substitute the value of \(x:\) \(-3\left(y-4\right)+3y=12\) - step3: Simplify: \(12=12\) - step4: Calculate: \(\left(x,y\right) = \left(y-4,y\right),y \in \mathbb{R}\) - step5: Alternative Form: \(\textrm{Infinitely many solutions}\) The system of equations has infinitely many solutions. This means that the two equations are linearly dependent, and there are an infinite number of solutions that satisfy both equations.