If you say a system is consistent, it means that it can be solved.
If you say a system is inconsistent, it means that the system has no solution.
If a system is dependent, it has infinite solutions and if it is independent, it has a unique solution. Both dependent and independent systems are consistent.
Each pair (a,1-a) is a solution,
for example, (1,0),(0,1),(-3,4),(2011,-2010),(e,1-e).
So, the system is consistent&dependent.