Problem
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. Keypad Keyboard Shortcuts Selecting an option will display any text boxes needed to complete your answer. No Solution Prev One Solution Solution Set \{ Infinitely Many Solutions
Solution
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 \(\boxed{x = 2y + 6}\).
