Solve by the elimination method. \( \begin{array}{r}5 x+6 y=3 \\ 10 x+12 y=6\end{array} \) \( \begin{array}{r}\text { Select the correct choice below and, if necessary, fill in the answer box to complete your choice. } \\ \text { A. The solution is } \\ \text { (Simplify your answer. Type an ordered pair.) } \\ \text { B. There are infinitely many solutions. } \\ \text { C. There is no solution. }\end{array} \)

To solve the system of equations by elimination, we start with: 1. \(5x + 6y = 3\) (Equation 1) 2. \(10x + 12y = 6\) (Equation 2) If we notice, Equation 2 is simply double Equation 1. This means both equations represent the same line and thus have infinitely many solutions. Let's look at our options: A. The solution is (Simplify your answer. Type an ordered pair.) B. There are infinitely many solutions. C. There is no solution. The correct choice is **B. There are infinitely many solutions.**