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If the system of equations aligned & ( -1) x+( -4) y+ z=5 & x+( -1) y+( -4) z=7 & ( +1) x+( +2) y-( +2) z=9 aligned has infinitely many solutions, then ^2+ is equal to

Options

  1. A6
  2. B10
  3. C20
  4. D12

Correct answer

D. 12

Step-by-step solution

aligned & ( -1) x+( -4) y+ z=5 & x+( -1) y+( -4) z=7 & ( +1) x+( +2) y-( +2) z=9 aligned For infinitely many solutions aligned & D = | array ccc -1 & -4 & & -1 & -4 +1 & +2 & -( +2) array |=0 & ( -3)(2 +1)=0 & D _ x = | array ccc 5 & -4 & 7 & -1 & -4 9 & +2 & -( +2) array |=0 & 2(3- )(23-2 )=0 & =3 & ^2+ =9+3=12 aligned

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