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How many solutions does the system of equations below have?\newline−3x−3y+3z=−2-3x - 3y + 3z = -2\newlinex+y−z=−1x + y - z = -1\newline−x−y+z=−7-x - y + z = -7\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?\newline−3x−3y+3z=−2-3x - 3y + 3z = -2\newlinex+y−z=−1x + y - z = -1\newline−x−y+z=−7-x - y + z = -7\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions
  1. Addition to Eliminate Variables: First, let's add the second and third equations to eliminate xx and yy. \newline(x+y−z)+(−x−y+z)=−1+(−7)(x + y - z) + (-x - y + z) = -1 + (-7)\newlineThis simplifies to 0x+0y+0z=−80x + 0y + 0z = -8, which is a contradiction since 00 cannot equal −8-8.
  2. Identifying Contradiction: Since we have a contradiction, it means that the system of equations has no solution.

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