If the line ax-2y + 2 = 0 is parallel to the line x + (A-3) y + 1 = 0, then the real number J? Find the real number a?

If the line ax-2y + 2 = 0 is parallel to the line x + (A-3) y + 1 = 0, then the real number J? Find the real number a?

Because parallel, then
a/1=-2/(a-3)
a(a-3)=-2
a^2-3a+2=0
(a-2)(a-1)=0
A = 2 or a = 1

The real number a = 0 is a ()
A. Sufficient condition B. necessary condition C. sufficient and necessary condition D. neither sufficient nor necessary condition
Why C is the answer, and how to calculate it

A = 0, y = - 1 / 2 is parallel to y = - 3 / 2, so it is a sufficient condition
Ax-2y = 1 is parallel to the line 2ax-2y = 3,
If a is not equal to 0, then the slope a / 2 = A and there is no real number a
So a = 0, necessary condition
Choose C
Y = - 1 / 2 and y = - 3 / 2 represent two straight lines parallel to the X axis. Of course, they are parallel

If the line L1: x a ^ 2Y 1 = 0 is parallel to the line L2: ax-2y-1 = 0, then the real number a uses two methods
If the line L1: x + A ^ 2Y + 1 = 0 is parallel to the line L2: ax-2y-1 = 0, then the real number a uses two methods

When a = 0, two lines are parallel
When a is not equal to 0
1. Straight line 1
y=(-1/a^2)x-1/a^2
Straight line 2
y=(a/2)x-1/2
therefore
-1/a^2=a/2
A = - cubic root 2
2. Straight line 1 passing through point
（0,-1/a^2),(-1,0)
Straight line 2 passing through point
(0,-1/2),(1/a,0)
therefore
1/a^2=-a/2
A = - cubic root 2