What is the solution of the system? y = -4x +4 y = -4x - 5

Since these two lines have the same slope, and different y-intercept, they are parallel lines, and will never intersect to make a solution.

This system has no solution....if we subtracted the second equation from the first, we obtain

0 = 9

Since this is impossible.....no solution exists

$${\mathtt{\,-\,}}{\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{4}} = {\mathtt{\,-\,}}{\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{5}}$$ if you add 4x to each side to negate the -4x on each side you get 4 = -5 which is incorrect so the answer is undefined, to diplay this on a graph it would be a verticle line.