\( \left. \begin{array} { c } { 9 y = - 4 x + 48 } \\ { 27 y + 12 x = - 72 } \\ \hline \end{array} \right. \)

To solve the system of equations, let's first rewrite them for clarity. 1. The first equation can be simplified: \[ 9y = -4x + 48 \implies y = \frac{-4x + 48}{9} \] 2. The second equation: \[ 27y + 12x = -72 \] We can solve this system using substitution or elimination. Let’s take the substitution method. Substituting \(y\) from the first equation into the second equation: \[ 27\left(\frac{-4x + 48}{9}\right) + 12x = -72 \] Multiplying everything out gives us: \[ 3(-4x + 48) + 12x = -72 \implies -12x + 144 + 12x = -72 \] Simplifying this: \[ 144 = -72 \] This leads us to an inconsistency, indicating that the two equations are parallel lines. Thus, they do not intersect, and the solution set is empty—there are no solutions to this system of equations!