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$\esthree{x = 1 y}{y = 7 z}{z = 3 x} $
Solve for x, y, z
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x=y
Calculate x from x=1y.
z=3y
Substitute y for x in the equation z=3x.
z=3\times 7z
Substitute 7z for y in the equation z=3y.
z=0
Solve z=3\times 7z for z.
y=7\times 0
Substitute 0 for z in the equation y=7z.
y=0
Calculate y from y=7\times 0.
x=0
Substitute 0 for y in the equation x=y.
x=0 y=0 z=0
The system is now solved.