How many solutions does the system of equations below have? \[ \begin{array}{l} 3 x-6 y=-7 \\ 6 x-12 y=-14 \end{array} \] no solution one solution Infinitely many solutions Submit

Step 1 ：The given system of equations is: 1. 3x - 6y = -7 2. 6x - 12y = -14

Step 2 ：We can see that the second equation is just the first equation multiplied by 2. This means that the two equations are not independent, they are the same line.

Step 3 ：Therefore, the system of equations does not have a unique solution. It either has no solutions or infinitely many solutions.

Step 4 ：To determine which of these is the case, we can check if the right-hand side of the equations are also multiples of each other. If they are, then the system has infinitely many solutions. If they are not, then the system has no solutions.

Step 5 ：In this case, -14 is indeed 2 times -7, so the system has infinitely many solutions.

Step 6 ：Final Answer: The system of equations has \(\boxed{\text{Infinitely many solutions}}\).