To solve for the solution of this system of equations,there are many ways to go about doing it, finding the point where the lines both intersect at.
One of the easiest is substitution, so plug in either one of the equations for the other one.
Y = X+4
Y = -4 + X
X+4 = -4 + X
Then solve for the X value to obtain the X coordinate of the point.
X+4 = -4 + X
X - X + 4 + 4 = -4 + 4 + X - X
8 = 0.
Since after trying to solve for X, we couldn't solve for it, and instead gave us numbers that are not equal to each other, there is no solution to these systems of equations, in other words, they don't intersect at a particular point.