A = 3 is a line ax + 2Y + 3A = 0 and a line 3x + (A-1) y = A-7 which are parallel and not coincident () A. Sufficient and nonessential condition B. necessary and nonessential condition C. sufficient and necessary condition D. neither sufficient nor necessary condition

A = 3 is a line ax + 2Y + 3A = 0 and a line 3x + (A-1) y = A-7 which are parallel and not coincident () A. Sufficient and nonessential condition B. necessary and nonessential condition C. sufficient and necessary condition D. neither sufficient nor necessary condition

When a = 3, the two lines are: 3x + 2Y + 9 = 0, 3x + 2Y + 4 = 0, the slopes of the two lines are equal, then they are parallel and not coincident. If the two lines are parallel and not coincident, then A3 = 2A − 1 ≠ 3a − 7 − a  a = 3. In conclusion, a = 3 is a necessary and sufficient condition for the two lines to be parallel and not coincident