2 How many solutions does the system \( \left\{\begin{array}{l}3 x+6 y=18 \\ 6 x+12 y=36\end{array}\right. \) have? (A) 0 (B) 1 (a) 2 (D) Infinite number

We are given the system: \[ \begin{cases} 3x + 6y = 18 \\ 6x + 12y = 36 \end{cases} \] **Step 1.** Notice that the second equation is exactly twice the first equation: \[ 2(3x+6y)=6x+12y \] and \[ 2(18)=36. \] **Step 2.** Since the second equation does not provide any new information (it is just a multiple of the first), both equations represent the same line. **Step 3.** Therefore, there are infinitely many solutions since any \((x, y)\) that satisfies the first equation will also satisfy the second. The correct answer is: (D) Infinite number.