The idea of elimination is to convert 3 equations with 3 variables to 2 equations with 2 variables, then to 1 equation with 1 variable.
Solve the following system of equations by elimination:
x−4y+z=−12x - 4y + z = -12x−4y+z=−12
x+3y−z=6x + 3y - z = 6x+3y−z=6
2x−2y+z=52x - 2y + z = 52x−2y+z=5
4x−3y+2z=204x - 3y + 2z = 204x−3y+2z=20
−2x−4y+3z=3-2x - 4y + 3z = 3−2x−4y+3z=3
x+y−z=2x + y - z = 2x+y−z=2
x+4y+7z=109x + 4y + 7z = 109x+4y+7z=109
4x−5y+4z=−294x - 5y + 4z = -294x−5y+4z=−29
5x+y−z=105x + y - z = 105x+y−z=10
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