System of equations - Math Central

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Question from chris, a student:

Find all real solutions (x,y,z,w) of the system of equations:
2y= x + x/17
2z= y + y/17
2w = z + z/17
2x= w + w/17

Chris,

2y = x + x/17
2y = 18/17 x

and thus

y = 18/34 x.

Likewise

z = 18/34 y
w = 18/34 z
x = 18/34 w.

Hence

x = 18/34 w
x = 18/34(18/34 z)
x = 18/34(18/34(18/34 y))
x = 18/34(18/34(18/34(18/34 x))).

Thus

x = (18⁴/ 34⁴) x.

Solve for x.

Penny

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