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Solve the system of equations by elimination.\newline−x−3y+3z=−11-x - 3y + 3z = -11\newlinex+2y+z=2x + 2y + z = 2\newline3x−2y+2z=03x - 2y + 2z = 0

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Q. Solve the system of equations by elimination.\newline−x−3y+3z=−11-x - 3y + 3z = -11\newlinex+2y+z=2x + 2y + z = 2\newline3x−2y+2z=03x - 2y + 2z = 0
  1. Eliminate xx by adding equations: Add the first and second equations to eliminate xx.
    (−x−3y+3z)+(x+2y+z)=−11+2(-x - 3y + 3z) + (x + 2y + z) = -11 + 2
    −x+x−3y+2y+3z+z=−9-x + x - 3y + 2y + 3z + z = -9
    −y+4z=−9-y + 4z = -9
  2. Prepare to eliminate xx: Multiply the second equation by 33 to prepare to eliminate xx with the third equation.\newline3(x+2y+z)=3(2)3(x + 2y + z) = 3(2)\newline3x+6y+3z=63x + 6y + 3z = 6
  3. Correct previous mistake: Add the new equation from Step 33 to the third equation to eliminate xx.(3x+6y+3z)+(3x−2y+2z)=6+0(3x + 6y + 3z) + (3x - 2y + 2z) = 6 + 03x+3x+6y−2y+3z+2z=63x + 3x + 6y - 2y + 3z + 2z = 66x+4y+5z=66x + 4y + 5z = 6
  4. Correct previous mistake: Add the new equation from Step 33 to the third equation to eliminate xx.\newline(3x+6y+3z)+(3x−2y+2z)=6+0(3x + 6y + 3z) + (3x - 2y + 2z) = 6 + 0\newline3x+3x+6y−2y+3z+2z=63x + 3x + 6y - 2y + 3z + 2z = 6\newline6x+4y+5z=66x + 4y + 5z = 6Oops, I made a mistake in the previous step. I should have subtracted the equations, not added them. Let's correct that.\newline(3x+6y+3z)−(3x−2y+2z)=6−0(3x + 6y + 3z) - (3x - 2y + 2z) = 6 - 0\newline3x−3x+6y+2y+3z−2z=63x - 3x + 6y + 2y + 3z - 2z = 6\newline8y+z=68y + z = 6

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