One solution

infinitely many solutions

no solution

y = 4x + 8
y = 5x + 1

Well, let's think about what a "solution" entails here.
A solution is going to be a point at which these two lines cross.
One solution will happen if the lines cross once.
Infinitely many solutions will occur if the lines are the same.
No solution occurs if the lines are parallel.
The second line can't be reduced in any way to be equivalent to the first (and vice versa), so we can rule out infinitely many solutions.
The two lines have different slopes and are thus not parallel to one another, ruling out no solution.
Thus, there is only one solution.
You can graph to find this solution, or solve this system using substitution. 
Using substitution, we know that y=y, and since we know that y=4x+8 as well as y=5x+1, we can set 4x+8 = 5x+1 and solve.
4x+8=5x+1
-4x -1  -4x -1
7=x
x=7
so when x=7, the lines will intercept. Let's get a y-value in there too.
You can plug the x-value into either equation, the result will be the same.
y = 4(7)+8
y = 5(7)+1
In both cases, y = 36.
So, at (7,36), both lines intercept. Thus, that is our only solution.

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