Solve the following system by the inverse matrix method, if possible. If the inverse matrix method doesn't apply, use any other method to determine if the system is inconsistent or dependent. If there is a solution, write your answer in the format $(x, y)$.
\[
\left\{\begin{array}{c}
-2 x+4 y=-12 \\
8 x-16 y=48
\end{array}\right.
\]
Answer 10 Points.
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Solution Set \{
Infinitely Many
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Answer
Final Answer: The system of equations has infinitely many solutions, and they can be represented as \(\boxed{x = 2y + 6}\).
Step 1 ：The given system of equations is: \(-2x + 4y = -12\) and \(8x - 16y = 48\).
Step 2 ：We can observe that the second equation is just the first equation multiplied by -4.
Step 3 ：This implies that the two equations are not independent, they are the same line.
Step 4 ：Therefore, the system of equations has infinitely many solutions.
Step 5 ：The solutions can be represented as \(x = 2y + 6\).
Step 6 ：Final Answer: The system of equations has infinitely many solutions, and they can be represented as \(\boxed{x = 2y + 6}\).
