Firstly, we'll substitute the ordered pair (1, -4) into both equations of the system. This will help us verify if the pair satisfies both equations.
Let's start with the first equation in the system, x - 2y = 8.
Substituting x = 1 and y = -4 into the first equation, we get:
1 - 2(-4) = 1 + 8 = 9
As you can see, 9 doesn't equal 8, so the ordered pair (1, -4) does not make the first equation true.
Next let's substitute into the second equation, 4x - y = 8.
Substituting x = 1 and y = -4 into the second equation, we get:
4(1) - (-4) = 4 + 4 = 8
In this case, 8 does equal 8, so the ordered pair (1, -4) does make the second equation true.
However, in order for an ordered pair to be a solution to a system of equations, it must satisfy all the equations in the system.
Since the ordered pair (1, -4) does not satisfy the first equation, we can conclude that it is not a solution to the system, despite the fact that it satisfies the second equation.