How many different values of a for which the system of equations
and has only one solution?
From the second equation, we have . Substituting into the first equation gives
For there to only be one solution, the discriminant must be 0, so
Checking the discriminant of this quadratic tells us how many values of a satisfy this equation, and therefore tell us how many values of a will give one solution to the original set of equations...
Since this is positive, there are two values of a which will satisfy the set of equations.