Answer:
Option A) Inconsistent is correct
Explanation:
Given equations are

and

Rewritting the equation y=5x+2 as below
5x-y=-2
Now multiplying the above equation into 2 we get

Now subtracting the equations (2) and (3)
10x-2y=12
10x-2y=-4
________

Therefore the given system of equations has no solution
Therefore it is inconsistent
Therefore given two lines are parallel. Two parallel lines never intersect, so the given system has no solution and is inconsistent.
Option A) Inconsistent is correct