Answer is (A),(D)
The given system of equations is
= 0 ⇒ at least one solution is possible.
Therefore, we have
• Option (A): The given set of equations are
That is, in this case, there is a unique solution. Hence, option (A) is correct.
• Option (B): The given set of equations are
However, this does not satisfy Eq. (1). Therefore, this system of equations has no solution. Hence, option (B) is incorrect.
Option (C): The given set of equations are
That is, this has infinitely many solutions. Hence, option (C) is incorrect.
• Option (D): The given set of equations are
That is, in this case, there is a unique solution. Hence, option (D) is correct.