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Solve the system of equations by elimination.\newline3x+2y+2z=−203x + 2y + 2z = -20\newline−x+2y−2z=−4-x + 2y - 2z = -4\newlinex+y+3z=2x + y + 3z = 2

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Solve a system of equations in three variables using eliminationright chevron icon

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Q. Solve the system of equations by elimination.\newline3x+2y+2z=−203x + 2y + 2z = -20\newline−x+2y−2z=−4-x + 2y - 2z = -4\newlinex+y+3z=2x + y + 3z = 2
  1. Add Equations: Step 11: Add the first and second equations to eliminate xx.3x+2y+2z=−203x + 2y + 2z = -20+(−x+2y−2z)=−4+ (-x + 2y - 2z) = -4‾\underline{\hspace{3em}}2x+4y=−242x + 4y = -24
  2. Multiply Third Equation: Step 22: Multiply the third equation by 33 to prepare to eliminate xx with the second equation.\newline3(x+y+3z)=3(2)3(x + y + 3z) = 3(2)\newline3x+3y+9z=63x + 3y + 9z = 6
  3. Add Modified Equations: Step 33: Add the modified third equation and the second equation to eliminate xx.3x+3y+9z=63x + 3y + 9z = 6+(−x+2y−2z)=−4+ (-x + 2y - 2z) = -4-------------------2x+5y+7z=22x + 5y + 7z = 2

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