1.
An ordered pair (α,β)(\alpha, \beta) for which the system of linear equations
(1+α)x+βy+z=2,(1+\alpha)x + \beta y + z = 2,

αx+(1+β)y+z=3,\alpha x + (1+\beta) y + z = 3,

αx+βy+2z=2\alpha x + \beta y + 2z = 2

has a unique solution, is: