\left\{ \begin{array} { l } { 2 x + 3 y - z = 20 } \\ { 3 x + 2 y + z = 20 } \\ { x + 4 y + 2 z = 10 } \end{array} \right.
Solve for x, y, z
x=6
y=2
z=-2
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z=2x+3y-20
Solve 2x+3y-z=20 for z.
3x+2y+2x+3y-20=20 x+4y+2\left(2x+3y-20\right)=10
Substitute 2x+3y-20 for z in the second and third equation.
y=8-x x=10-2y
Solve these equations for y and x respectively.
x=10-2\left(8-x\right)
Substitute 8-x for y in the equation x=10-2y.
x=6
Solve x=10-2\left(8-x\right) for x.
y=8-6
Substitute 6 for x in the equation y=8-x.
y=2
Calculate y from y=8-6.
z=2\times 6+3\times 2-20
Substitute 2 for y and 6 for x in the equation z=2x+3y-20.
z=-2
Calculate z from z=2\times 6+3\times 2-20.
x=6 y=2 z=-2
The system is now solved.
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