Graphing is a crutch... :P It is simpler to solve mathematically...
If a solution exists the coordinate pairs will be equal so we can say y=y so:
5x+1=x-3 subtract 1 from both sides
5x=x-4 subtract x from both sides
4x=-4 divide both sides by 4
x=-1, now using this x in either original equation you can solve for y....
y=x-3 becomes, y=-1-3=-4
So the solution to the system is the point (-1,-4)
Graphically this is the point where the two lines intersect.
