Determine whether the system is consistent, inconsistent, or dependent.

2x + 2y = 2
6x + 6y = 6 or consistent and dependent

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.

To determine whether a system of equations is consistent, inconsistent, or dependent, we need to analyze the coefficients and constants in the equations.

The given system of equations is:
1) 2x + 2y = 2
2) 6x + 6y = 6

To check if the system is consistent or inconsistent, we need to compare the left-hand sides (LHS) and right-hand sides (RHS) of the equations. In this case, both equations have the same RHS, which is 2 on the LHS.

The ratio of the coefficients in equation 1 to equation 2 is:
2/6 = 1/3

Since the ratios of the coefficients are equal and the ratio of the RHS is also equal, this means that the two equations represent the same line in the plane. Therefore, the system is dependent.

In conclusion, the system of equations is consistent and dependent.