An ordered pair  α,β for which the system of linear equations 1+αx+βy+z=2αx+1+βy+z=3ax+βy+2z=2Has a unique solution , is

Given system of linear equations , (1+α)x+βy+z=2αx+(1+β)y+z=3αx+βy+2z=2Has a unique solution , if 1+αβ1α1+β1αβ2≠0 Apply R1→R1−R3 and R2→R2−R310−101−1αβ2≠0⇒1(2+β)−0(0+α)−1(0−α)≠0⇒ α+β+2≠0 ……(i)Note that, only (2,4) satisfy the Eq . (i)