Put them both into slope intercept form and examine the slopes.
If the slopes are different, there is only one solution.
If the slopes are the same, examine the vertical intercepts.
If the intercepts are the same it has infinitely many solutions, if the intercepts are different it has no solutions.
4x + 8y = 16 ⇔ x + 2y = 4
3x + 6y = 9 ⇔ x + 2y = 3
Equations contradict each other (4 = 3).
Therefore, system has no solution.
