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How many solutions does the system of equations below have?\newline2x−3y+z=92x - 3y + z = 9\newline−2x−3y+2z=−18-2x - 3y + 2z = -18\newline−2x+2y+2z=12-2x + 2y + 2z = 12\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions

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Q. How many solutions does the system of equations below have?\newline2x−3y+z=92x - 3y + z = 9\newline−2x−3y+2z=−18-2x - 3y + 2z = -18\newline−2x+2y+2z=12-2x + 2y + 2z = 12\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions
  1. Eliminate x: First, let's add the first and second equations to eliminate x.\newline(2x−3y+z)+(−2x−3y+2z)=9−18(2x - 3y + z) + (-2x - 3y + 2z) = 9 - 18\newlineThis simplifies to −6y+3z=−9-6y + 3z = -9.
  2. Eliminate x again: Now, let's add the first and third equations to eliminate x again.\newline(2x−3y+z)+(−2x+2y+2z)=9+12(2x - 3y + z) + (-2x + 2y + 2z) = 9 + 12\newlineThis simplifies to −y+3z=21-y + 3z = 21.
  3. Eliminate y: We can multiply the second simplified equation by 22 and add it to the first simplified equation to eliminate yy.
    (−6y+3z)+2(−y+3z)=−9+2(21)( -6y + 3z ) + 2( -y + 3z ) = -9 + 2(21)
    This simplifies to −6y+3z−2y+6z=−9+42-6y + 3z - 2y + 6z = -9 + 42

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