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Given the system of equations:\newlinex−3y−2z=−11 x - 3y - 2z = -11 \newline2x+2y+2z=2 2x + 2y + 2z = 2 \newline2x−2y−z=2 2x - 2y - z = 2

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Q. Given the system of equations:\newlinex−3y−2z=−11 x - 3y - 2z = -11 \newline2x+2y+2z=2 2x + 2y + 2z = 2 \newline2x−2y−z=2 2x - 2y - z = 2
  1. Combine Equations to Eliminate z: First, let's add the first and third equations to eliminate zz.
    (x−3y−2z)+(2x−2y−z)=−11+2(x - 3y - 2z) + (2x - 2y - z) = -11 + 2
    3x−5y−3z=−93x - 5y - 3z = -9
  2. Combine Equations to Eliminate z: Next, let's add the second and third equations to eliminate zz. \newline(2x+2y+2z)+(2x−2y−z)=2+2(2x + 2y + 2z) + (2x - 2y - z) = 2 + 2 \newline4x+z=44x + z = 4
  3. Solve for z z : Now, let's solve for z z from the second equation. z=4−4x z = 4 - 4x
  4. Substitute z z into First Equation: Substitute z=4−4x z = 4 - 4x into the first equation. x−3y−2(4−4x)=−11 x - 3y - 2(4 - 4x) = -11 x−3y−8+8x=−11 x - 3y - 8 + 8x = -11 9x−3y−8=−11 9x - 3y - 8 = -11 9x−3y=−3 9x - 3y = -3
  5. Simplify First Equation: Simplify the equation. 3x−y=−13x - y = -1
  6. Substitute zz into Third Equation: Now, substitute z=4−4xz = 4 - 4x into the third equation.2x−2y−(4−4x)=22x - 2y - (4 - 4x) = 2 2x−2y−4+4x=22x - 2y - 4 + 4x = 2 6x−2y−4=26x - 2y - 4 = 2 6x−2y=66x - 2y = 6
  7. Simplify Third Equation: Simplify the equation. 3x−y=33x - y = 3
  8. Final Equations: We have two equations now: 3x−y=−13x - y = -1 3x−y=33x - y = 3

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