Prove that there is a value of c (≠ 0) for which the system

Has infinitely many solutions. Find this value.

For what value of a, the system of equations is inconsistent

ax + 3y = a - 3

12x + ay = a

Find the value of k for which the system

has (i) a unique solution, and (ii) no solution.

Find the values of k for which the system

Will have (i) a unique solution and (ii) no solution. Is there a value of k for which the system has infinitely many solutions?

For what value of k, the following system of equations will represent the coincident lines?