Solve the system by the addition method. \[ \begin{array}{l} 3 x=4 y+5 \\ 6 x=-1-5 y \end{array} \] 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. Use integers or fractions for any numbers in the expression.) B. There are infinitely many solutions. C. There is no solution.

Step 1 ：Given the system of equations: \[\begin{array}{l} 3 x=4 y+5 \\ 6 x=-1-5 y \end{array}\]

Step 2 ：We can multiply the first equation by 2 to get: \[6x = 8y + 10\]

Step 3 ：Adding the two equations together, we get: \[12x = 3y + 9\]

Step 4 ：Solving for x, we get: \[x = \frac{y}{4} + \frac{3}{4}\]

Step 5 ：Substituting x into one of the original equations, we can solve for y to get: \[y = -\frac{11}{13}\]

Step 6 ：Substituting y back into the equation for x, we get: \[x = \frac{3}{4}\]

Step 7 ：Final Answer: The solution set is \(\boxed{\left(\frac{3}{4}, -\frac{11}{13}\right)}\)