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Solve the system of equations by elimination.\newline2x+3y−2z=102x + 3y - 2z = 10\newline3x−2y−z=−63x - 2y - z = -6\newline−3x−2y−2z=10-3x - 2y - 2z = 10

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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.\newline2x+3y−2z=102x + 3y - 2z = 10\newline3x−2y−z=−63x - 2y - z = -6\newline−3x−2y−2z=10-3x - 2y - 2z = 10
  1. Eliminate x: First, let's add the second and third equations to eliminate x.\newline(3x−2y−z)+(−3x−2y−2z)=−6+10(3x - 2y - z) + (-3x - 2y - 2z) = -6 + 10\newline3x−2y−z−3x−2y−2z=43x - 2y - z - 3x - 2y - 2z = 4\newline−4y−3z=4-4y - 3z = 4
  2. Eliminate z: Now, let's multiply the first equation by 33 and the second equation by 22 so we can eliminate zz by adding them.\newline(2x+3y−2z)×3=10×3(2x + 3y - 2z) \times 3 = 10 \times 3\newline(3x−2y−z)×2=−6×2(3x - 2y - z) \times 2 = -6 \times 2\newline6x+9y−6z=306x + 9y - 6z = 30\newline6x−4y−2z=−126x - 4y - 2z = -12
  3. Eliminate z: Add the modified equations to eliminate z.\newline(6x+9y−6z)+(6x−4y−2z)=30+(−12)(6x + 9y - 6z) + (6x - 4y - 2z) = 30 + (-12)\newline6x+9y−6z+6x−4y−2z=186x + 9y - 6z + 6x - 4y - 2z = 18\newline12x+5y−8z=1812x + 5y - 8z = 18
  4. Eliminate z: Now we have two new equations without z:\newline−4y−3z=4-4y - 3z = 4\newline12x+5y−8z=1812x + 5y - 8z = 18\newlineLet's multiply the first equation by 22 and add it to the second equation to eliminate z.\newline(−4y−3z)×2=4×2(-4y - 3z) \times 2 = 4 \times 2\newline−8y−6z=8-8y - 6z = 8\newline12x+5y−8z=1812x + 5y - 8z = 18
  5. Eliminate z: Now we have two new equations without z:\newline−4y−3z=4-4y - 3z = 4\newline12x+5y−8z=1812x + 5y - 8z = 18\newlineLet's multiply the first equation by 22 and add it to the second equation to eliminate z.\newline(−4y−3z)×2=4×2(-4y - 3z) \times 2 = 4 \times 2\newline−8y−6z=8-8y - 6z = 8\newline12x+5y−8z=1812x + 5y - 8z = 18Add the modified equations to eliminate z.\newline(−8y−6z)+(12x+5y−8z)=8+18(-8y - 6z) + (12x + 5y - 8z) = 8 + 18\newline−8y−6z+12x+5y−8z=26-8y - 6z + 12x + 5y - 8z = 26\newline12x−3y−14z=2612x - 3y - 14z = 26

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