Final answer:
The system of equations -3x + 6y = -4 and -6x + 12y = -8 are dependent and consistent, meaning they represent the same line and thus have infinite solutions. There is no unique solution to this system.
Step-by-step explanation:
To solve the system of equations -3x + 6y = -4 and -6x + 12y = -8 using substitution or elimination, we first observe that these two equations are multiples of each other. The second equation is precisely two times the first. This suggests that every solution to the first equation will also be a solution to the second and, therefore, these equations are dependent, meaning there are infinite solutions that lie along the same line.
The system is consistent and dependent, but we cannot find a unique solution for the values of x and y.
To illustrate with elimination: If we try to subtract the first equation from the second, after multiplying the first equation by 2, we get:
2(-3x + 6y) = 2(-4)
-6x + 12y = -8
- (-6x + 12y) = -(-8)
0 = 0
This just confirms that the equations are indeed multiples of one another and do not allow for a unique solution.