The system has no solution. The system has a unique solution: $(x, y)=(\square, \square)$ \[ \begin{array}{r} -x+4 y=-8 \\ x-4 y=-8 \end{array} \] The system has infinitely many solutions. They must satisfy the following equation: \[ y= \]

Step 1 ：The given system of equations is: \(-x + 4y = -8\) and \(x - 4y = -8\)

Step 2 ：We can see that the second equation is just the first equation multiplied by -1. This means that the two equations are dependent and represent the same line.

Step 3 ：Therefore, the system has infinitely many solutions.

Step 4 ：To find the equation that the solutions must satisfy, we can solve one of the equations for y. Let's solve the first equation for y.

Step 5 ：The solution to the equation \(-x + 4y = -8\) for y is \(y = \frac{x}{4} - 2\). This is the equation that all solutions to the system must satisfy.

Step 6 ：Final Answer: The solutions to the system must satisfy the equation \[y = \boxed{\frac{x}{4} - 2}\]