each line represents all the pairs (x,y) that solve one of the two equations. For instance, (0,3), on the green line, solves the first equation, as does any other point on the green line. Every point on the second line solves the second equation.
The 'system' of equations is solved when both equations are true, so you just need to look at where the lines intersect. In this case, it's (2,4).