IF:
|1/2.x -2/3.y = 7 and
|a.x - 8.y = -1
have no solution, that means these 2 linear equations ARE PARALLEL (since they can never meet). Reminder: 2 equations are parallel if they have the same coefficient , so let write each of the equation in the normal form:
a)1/2.x -2/3.y = 7→ -2/3.y = -1/2.x + 7 → y = 3/4.x - 21/2
b) a.x - 8.y = -1 → - 8.y = -a.x - 1 → y= a/8.x + 1
a) and b) are // if (3/4) = (a/8), [the 2 coefficient OR the 2 slopes)
a/8 = 3/4 → a = 24/4 and a = 6 (Answer D)