Inconsistent -----------------------> parallel LINES

this is when a1/a2 = b1/b2 and not equal to c1/c2

when the coefficient in the variables are the same but different constant

http://www.algebra.com/algebra/homework/coordinate/Types-of-systems-inconsistent-dependent-independent.lesson  <---- for more info

This lesson concerns systems of two equations, such as: 

2x + y = 10

3x + y = 13.

The equations can be viewed algebraically or graphically. Usually, the problem is to find a solution for x and y that satisfies both equations simultaneously. Graphically, this represents a point where the lines cross. There are 3 possible outcomes to this (shown here in blue, green, and red):

The two lines might not cross at all, as in 


y = x
y = x + 10.

This means there are no solutions, and the system is called inconsistent. 

If you try to solve this system algebraically, you'll end up with something that's not true, such as 0 = 10. 

Whenever you end up with something that's not true, the system is inconsistent.