Solve the system by the substitution method. \[ \begin{array}{r} x+y=-12 \\ y=-4 x \end{array} \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Type an ordered pair.) B. There are infinitely many solutions. The solution set is $\{(x, y) \mid\}$. (Type an equation.) C. There is no solution. The solution set is $\varnothing$.

Step 1 ：The system of equations is given as: \[\begin{array}{r} x+y=-12 \\ y=-4 x \end{array}\]

Step 2 ：We can substitute \(y = -4x\) from the second equation into the first equation. This gives us a new equation in terms of x only: \(-3x = -12\).

Step 3 ：Solving this equation gives us the value of x: \(x = 4\).

Step 4 ：Substituting \(x = 4\) back into the second equation \(y = -4x\) gives us the value of y: \(y = -16\).

Step 5 ：Thus, the solution to the system of equations is \(\boxed{(4, -16)}\).