Answer: option A. 2x+8y=6 & 5x+20y=2
The reason why it is inconsistent is because it leads to an imposible (absurd) situation:
You can see it here:
2x + 8y = 6
5x + 20y = 2
Multiply the first equation by 5 and the second equation by 2:
10x + 40y = 30
10x + 40y = 4
Subtract the second from the first:
0 = 30 - 4
0 = 26 which is a contradiction. That means that the system cannot been solved, because none pair (x,y) can meet both equations.
You can realize that the option A is an inconsistent system if you find the slope of the two lines by dividing the coefficient of x by the coefficient of y, which is the slope of the line, for both equations, because they are equal, and then verify that they do not have the same y-intercept, meaning that they are parallel and never touch each other. When the graph of the two lines show that they do not intercept each other means that the system is inconsistent.
first equation: 2/8 = 1/4
second equation: 5/20 = 1/4