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How many solutions does the system of equations below have?\newline2x+y+2z=112x + y + 2z = 11\newline−2x−3y+3z=19-2x - 3y + 3z = 19\newline2x+3y−3z=152x + 3y - 3z = 15\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+y+2z=112x + y + 2z = 11\newline−2x−3y+3z=19-2x - 3y + 3z = 19\newline2x+3y−3z=152x + 3y - 3z = 15\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions
  1. Combine equations to eliminate xx: Add the first and third equations to eliminate xx.
    (2x+y+2z)+(2x+3y−3z)=11+15(2x + y + 2z) + (2x + 3y - 3z) = 11 + 15
    4x+4y−z=264x + 4y - z = 26
  2. Add equations to eliminate y: Now, add the second equation to the new equation we got from the first step.\newline(−2x−3y+3z)+(4x+4y−z)=19+26(-2x - 3y + 3z) + (4x + 4y - z) = 19 + 26\newline2x+y+2z=452x + y + 2z = 45

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