For which values of "a" will the following system have no solutions?

exactly one solution?

infinitely many solutions?

Set up the system in matrix form: AX = B where A is the coefficient matrix.

There's a unique solution if \(\displaystyle det(A) \neq 0\).

If \(\displaystyle det(A) = 0\) then there is either no solution or an infinite number of solutions. You need to examine this situation closely to decide.

Alternatively, you can set up the augmented matrix and do row operations. Then note that a row looking like 0 0 0 | 0 means infinite solutions and a row looking like 0 0 0 | * where * is not zero means no solutions. Otherwise there is a unique solution.

Details of the theory briefly outlined above are certain to be in your classnotes and textbook. If you need more help please show all that you have tried and say where you get stuck.