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Solve for x, y, z
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x=1-y
Solve x+y=1 for x.
2\left(1-y\right)+y=1 1-y+y+z=1
Substitute 1-y for x in the second and third equation.
y=1 z=0
Solve these equations for y and z respectively.
x=1-1
Substitute 1 for y in the equation x=1-y.
x=0
Calculate x from x=1-1.
x=0 y=1 z=0
The system is now solved.