Final answer:
To classify the system, we solve the equations and determine if a solution exists or not. In this case, the system is inconsistent because the equations lead to a contradiction.
Step-by-step explanation:
To classify the system without graphing, we can use the technique of solving the system of equations.
Given the system:
{2x = y - 7
4x - 2y + 4 = 0}
We can solve the first equation for y:
y = 2x + 7
Substitute this value of y into the second equation:
4x - 2(2x + 7) + 4 = 0
Simplify the equation:
4x - 4x - 14 + 4 = 0
-14 = 0
This is a contradiction since -14 does not equal 0.
Therefore, the system is inconsistent.
The correct answer is C. inconsistent.