Solve the system by the method of your choice. \( \begin{array}{r}4 x=y-2 \\ 4 x-y=9\end{array} \) 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. C. There is no solution.

Let's solve the system of equations step by step. 1. From the first equation \(4x = y - 2\), we can express \(y\) in terms of \(x\): \[ y = 4x + 2 \] 2. Next, we substitute \(y\) in the second equation \(4x - y = 9\): \[ 4x - (4x + 2) = 9 \] Simplifying, we have: \[ 4x - 4x - 2 = 9 \] \[ -2 = 9 \] Since the above statement is false, it indicates that there are no values for \(x\) and \(y\) that satisfy both equations simultaneously. Therefore, the answer is: C. There is no solution.