Solve the system by the addition method. \[ \begin{array}{l}2 x+14 y=2 \\ 4 x-14 y=4\end{array} \] 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.

To solve the system using the addition method, we can first align the two equations as: 1. \( 2x + 14y = 2 \) 2. \( 4x - 14y = 4 \) Next, we can manipulate the first equation by multiplying it by 2 to align the coefficients of \(x\): \( 4x + 28y = 4 \) Now we have the system: 1. \( 4x + 28y = 4 \) 2. \( 4x - 14y = 4 \) Next, we can subtract the second equation from the first: \[ (4x + 28y) - (4x - 14y) = 4 - 4 \] This simplifies to: \[ 42y = 0 \] Thus, we find \(y = 0\). Now substitute \(y = 0\) back into the first equation to find \(x\): \[ 2x + 14(0) = 2 \quad \Rightarrow \quad 2x = 2 \quad \Rightarrow \quad x = 1 \] So we get the solution: \(\{(1, 0)\}\). The correct choice is A. The solution set is \{(1, 0)\}.