3x+y=4 and 6x+2y=8 has many solutions because 6x+2y=8 is the same as 3x+y=4 (doubling an equation doesn't change the equality).
3x+y=4 can be written y=4-3x, that is, y depends on x (or vice versa). Choose any value for x and you get an associated value for y. The relationship can be represented by a straight line graph, where every point on the line represents a solution to 3x+y=4, an infinite number of solutions.