Final answer:
The system of equations is dependent, resulting in infinitely many solutions after applying the elimination method.
Step-by-step explanation:
We need to solve the system of equations by elimination:
3x - 6y = 15
2x - 4y = 10
To use elimination, we first make sure that the coefficients of one of the variables are the same or opposites. In this case, the coefficients of y are already multiples of each other (-6 and -4). We can multiply the second equation by 1.5 to get the coefficients of y to match:
1.5(2x - 4y) = 1.5(10)
3x - 6y = 15 (no change here)
This gives us:
3x - 6y = 15
3x - 6y = 15
It appears that after multiplying, we just have two identical equations, which implies the system has infinitely many solutions or is a dependent system where every solution to one equation is also a solution to the other.