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Solve the system of equations by elimination.\newline−3x+2y−z=−16-3x + 2y - z = -16\newline−3x+y−2z=−20-3x + y - 2z = -20\newlinex+2y−2z=6x + 2y - 2z = 6

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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.\newline−3x+2y−z=−16-3x + 2y - z = -16\newline−3x+y−2z=−20-3x + y - 2z = -20\newlinex+2y−2z=6x + 2y - 2z = 6
  1. Add Equations for Elimination: question_prompt: Solve the system of equations by elimination and find the values of xx, yy, and zz.
  2. Multiply Third Equation: Step 11: Add the first and second equations to eliminate xx.(−3x+2y−z)+(−3x+y−2z)=−16+(−20) (-3x + 2y - z) + (-3x + y - 2z) = -16 + (-20) −6x+3y−3z=−36 -6x + 3y - 3z = -36
  3. Add Equations for Elimination: Step 22: Multiply the third equation by 33 to prepare for elimination with the first equation.\newline3(x+2y−2z)=3(6)3(x + 2y - 2z) = 3(6)\newline3x+6y−6z=183x + 6y - 6z = 18
  4. Multiply Equation for Elimination: Step 33: Add the first and the new third equation to eliminate xx.(−3x+2y−z)+(3x+6y−6z)=−16+18 (-3x + 2y - z) + (3x + 6y - 6z) = -16 + 18 8y−7z=2 8y - 7z = 2
  5. Add Equations for Elimination: Step 44: Multiply the new equation from Step 11 by 22 to prepare for elimination with the new equation from Step 33.\newline2(−6x+3y−3z)=2(−36)2(-6x + 3y - 3z) = 2(-36)\newline−12x+6y−6z=−72-12x + 6y - 6z = -72
  6. Divide Equation for Simplification: Step 55: Add the new equation from Step 44 and the new third equation to eliminate xx.(−12x+6y−6z)+(3x+6y−6z)=−72+18 (-12x + 6y - 6z) + (3x + 6y - 6z) = -72 + 18 −9x+12y−12z=−54 -9x + 12y - 12z = -54
  7. Add Equations for Elimination: Step 66: Divide the new equation from Step 55 by −3-3 to simplify.\newline−9x−3+12y−3−12z−3=−54−3-\frac{9x}{-3} + \frac{12y}{-3} - \frac{12z}{-3} = \frac{-54}{-3}\newline3x−4y+4z=183x - 4y + 4z = 18
  8. Multiply Equation for Elimination: Step 77: Add the new equation from Step 66 and the second original equation to eliminate xx.(3x−4y+4z)+(−3x+y−2z)=18+(−20)(3x - 4y + 4z) + (-3x + y - 2z) = 18 + (-20)−3y+2z=−2-3y + 2z = -2
  9. Add Equations for Elimination: Step 88: Multiply the new equation from Step 33 by 33 to prepare for elimination with the new equation from Step 77.\newline3(8y−7z)=3(2)3(8y - 7z) = 3(2)\newline24y−21z=624y - 21z = 6
  10. Add Equations for Elimination: Step 88: Multiply the new equation from Step 33 by 33 to prepare for elimination with the new equation from Step 77.\newline3(8y−7z)=3(2)3(8y - 7z) = 3(2)\newline24y−21z=624y - 21z = 6 Step 99: Add the new equation from Step 77 and the new equation from Step 88 to eliminate zz.\newline(−3y+2z)+(24y−21z)=−2+6(-3y + 2z) + (24y - 21z) = -2 + 6\newline21y−19z=421y - 19z = 4

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