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Solve for x, y, z
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y=x x+\frac{1}{x}=2 z=y
Reorder the equations.
z=x
Substitute x for y in the equation z=y.
x=1
Solve x+\frac{1}{x}=2 for x.
z=1
Substitute 1 for x in the equation z=x.
y=1
Substitute 1 for x in the equation y=x.
x=1 y=1 z=1
The system is now solved.