For what value(s) of `alpha` will the system of linear equations `alphax + 3y = alpha - 3` and `12x + alpha y = alpha` has a unique solution?

Explanation

The given equations are
`alphax + 3y = alpha - 3`
`12x + alpha y = alpha`
Here `a_(1) = alpha, b_(1) = 3` and `c_(1) = alpha - 3`
`a_(2) = 12, b_(2) = alpha` and `c_(2) = alpha`
The system has a unique solution if `(a_(1))/(a_(2)) ne (b_(1))/(b_(2))`
`implies (alpha)/(12) ne (3)/(alpha)`
`implies a^(2) ne 36`
`implies alpha ne pm 6`
i.e., `a ne 6` and `alpha ne - 6`
So, `alpha` can take any real value except - 6 and 6.