If the lines x+y+1=0,4x+3y+4=0 and x+αy+β=0 where α2+β2=2 are concurrent then

The given lines are x+y+1=04x+3y+4=0x+αy+β=0If these lines are concurrent, then  1    1    14    3    41    α    β=0To solve the equation use elementary column operations C2→C2−C1,C3→C3−C11004−101α−1β−1=0 1(1−β−0)=0β=1Given  α2+β2=2⇒α2=1⇒α=±1Therefore α=±1 and β=1