If the system of equations array r 11 x+y+ z=-5 2 x+3 y+5 z=3 8 x-19 y-39 z= array has infinitely many solutions, then ^4- is equal to :

Step-by-step solution

aligned & 11 x+y+ z=-5 & 2 x+3 y+5 z=3 & 8 x-19 y-39 z= aligned for infinite sol. aligned & D = | array ccc 11 & 1 & 2 & 3 & 5 8 & -19 & -39 array |=0 & 11(-117+95)-1(-78-40)+ (-38-24) & 11(-22)+118- (62)=0 & 62 =118-242 & = -124 62 =-2 aligned aligned & D ₁= | array ccc -5 & 1 & -2 3 & 3 & 5 & -19 & -39 array |=0 & -5(-117+95)-1(-117-5 )-2(-57-3 )=0 & -5(-22)+117+5 +114+6 =0 & 11 =-110-231=-341 & =-31 & ^4- =(-2)^4-(-31)=16+31=47 aligned