Final answer:
Without the full system of equations, it's impossible to determine which value of 'a' would make the system inconsistent. We would typically use matrix operations to find out, but the provided information is insufficient to proceed.
Step-by-step explanation:
The question appears to be asking for the value of a variable 'a' which would make a system of equations inconsistent. An inconsistent system is one where there is no set of values that simultaneously satisfies all the equations in the system. However, without the actual system of equations provided, it's impossible to determine the value that makes the system inconsistent. Moreover, the miscellaneous details provided do not seem to relate to a system of equations or the steps to find inconsistency within such a system.
To assess inconsistency in a system of linear equations, you would typically transform the equations into an augmented matrix and then perform row operations to achieve row-echelon form. If a row in the matrix has all zero coefficients with a non-zero constant in the augmented portion, the system is inconsistent. Without the full equations, we cannot complete this process or provide a specific value of 'a'.