Solve the system by the method of your choice. \( \begin{array}{l}4 x=y-2 \\ 4 x-y=9\end{array} \) 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. The first equation is \(4x = y - 2\). We can rearrange it to express \(y\): \(y = 4x + 2\). Now we substitute \(y\) into the second equation \(4x - y = 9\): \(4x - (4x + 2) = 9\). Simplifying this gives: \(4x - 4x - 2 = 9\) \(-2 = 9\). This shows that we have reached a contradiction. Therefore, there is no solution to the system of equations. The correct choice is: C. There is no solution.