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If the system of equations aligned & x+2 y-3 z=2 & 2 x+ y+5 z=5 & 14 x+3 y+ z=33 aligned has infinitely many solutions, then + is equal to :

Options

  1. A13
  2. B10
  3. C12
  4. D11

Correct answer

C. 12

Step-by-step solution

aligned & = | array ccc 1 & 2 & -3 2 & & 5 14 & 3 & array |=0 +42 -4 +107=0 & ₁= | array ccc 2 & 2 & -3 5 & & 5 33 & 3 & array |=0 2 +99 -10 +255=0 & ₂= | array ccc 1 & 2 & -3 2 & 5 & 5 14 & 33 & array |=0 =13 aligned Also, =-1 Hence, + =13-1=12

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