Find the value of a. Could anyone smart teach me please?tks

Question

Let a be a non-zero constant. If the straight line L1:ax+2y+8=0, L2:4x+(a+2)y-6=0 and L3:y=0 cannot form a triangle, find the value of a

Answer 1

Given ax+2y+8=0, 4x+(a+2)y-6=0 and y=0
The value of a=2
Which is non-zore and the doesn't make triangle

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Answer 2

L1: ax+2y+8=0, L2: 4x+(a+2)y-6=0, L3: y=0

If a=-2, three lines can be rewritten: L1: y=x-4, L2: x=3/2, L2: y=0   These 3 lines have different slopes, and form a triangle.   Therefore, a≠0 and three lines can be rewritten as follows:

L1: y=-ax/2 - 4, L2: y=-4x/(a+2) + 6/(a+2), L3: y=0

Since a≠0 and a≠-2, L1 and L2 are not parallel to L3.   Thus, L1 and L2 must be parallel to each other not to form a triangle.   So, the slopes of L1 and L2 must be identical.  

That is: -a/2=-4/(a+2)   Simplify the equation, getting (a+4)(a-2)=0   We have: a=-4, or a=2

CK: Plug the values of a into the equations of L1 and L2.  

If a=-4, L1: y=2x - 4, L2: y=2x - 3/2, so L1 and L2 are parallel to each other.

If a=2, L1: y=-x - 4, L2: y=-x + 3/2, so L1 and L2 are parallel to each other.   CKD.

Therefore, the answer is: a=-4, or a=2