Find the values of a,b and c.?

If a < c , then L1 must NOT parallel to L2 since the slope of L1 = - a > the slope of L2 = - c.
By given 3 lines intersect at 2 points only , so L2 // L3 or L1 // L3.

The equation of the line passing through (0,-1) and (1,-4) is y + 3x + 1 = 0.
If L2 // L3 , then b = c , but this time L1 is y + 3x + 1 = 0 so a = 3 and b = 1 = c < a (contradiction).

It must be L1 // L3 , then a = b < c , hence L3 passing through (1 , -4) while L1 passing through (0 , -1).
We have a = b = 1 and c = 3 by solving L3: -4+b+c=0 and L1: -1+b=0.
Verify: L2: y + 3x + 1 = 0 passing through (0,-1) and (1,-4).