Solve the system by the addition method. \[ \begin{array}{r}4 x+12 y=8 \\ 3 x-12 y=6\end{array} \] Aelect the correct choice below and, if necessary, fill in the answer box to complete your choice. B. There are infinitely many solutions. C. There is no solution.

To solve the system of equations using the addition method, we first align the equations: 1. \( 4x + 12y = 8 \) 2. \( 3x - 12y = 6 \) Next, we can add these equations together. Notice that the \(12y\) and \(-12y\) will cancel out: \[ (4x + 12y) + (3x - 12y) = 8 + 6 \] This simplifies to: \[ 7x = 14 \] Now, we can solve for \(x\): \[ x = 2 \] Now we can substitute \(x = 2\) back into one of the original equations to find \(y\). Using the first equation: \[ 4(2) + 12y = 8 \] Which simplifies to: \[ 8 + 12y = 8 \] \[ 12y = 0 \Rightarrow y = 0 \] Thus, the solution to this system of equations is \(x = 2\) and \(y = 0\), so we have a unique solution: \((2, 0)\). Since we found a solution, the correct choice is that there is one unique solution. Hence, the answer is: A. There is a unique solution: \( (2, 0) \).