I did Gaussian elimination carefully and discovered that the coefficient matrix for the row reduced system of equations is invertible unless a = 2 or a = -1.

Then I checked that there is in fact no solution when a = -1. (We know b is not 0, because otherwise the given system of equations would always have a solution consisting of all zeros.)

print(-1)

-1 will be the answer

The determinant of the left hand side of the system reduces to D = 2a² - 2a - 4. For the system to have no solution, D = 0, solving the quadratic equation yields:

a² - a - 2 = 0;

(a + 1)(a - 2) = 0;

a = -1, a = 2

The least possible value of a is -1.

D = 2a² - 4 - 2a Regardless of b there is no solution for D=0 => a=[-1, 2]