x-elements of solve and the list "x"

Hello,

I try to make a list like "x" from the solve function as the following:

for i:1 thru 3 step 1 do
( K: solve([ i*x[i]^2+y[i]=2, i*x[i]^2+z[i]=2,
x[i]+2*i*y[i]=4],[x[i],y[i],z[i]]),
display(K),
display(x[i]));

The answer of Maxima is:
(%o27)
K=[[x[1]=1/2,y[1]=7/4,z[1]=7/4],[x[1]=0,y[1]=2,z[1]=2]]
x[1]=x[1]
K=[[x[2]=(sqrt(129)+1)/16,y[2]=-(sqrt(3)*sqrt(43)-63)/64,z[2]=-(sqrt(3)*sqrt(43)-63)/64],[x[2]=-(sqrt(129)-1)/16,y[2]=(sqrt(3)*sqrt(43)+63)/64,z[2]=(sqrt(3)*sqrt(43)+63)/64]]
x[2]=x[2]
K=[[x[3]=(sqrt(577)+1)/36,y[3]=-(sqrt(577)-143)/216,z[3]=-(sqrt(577)-143)/216],[x[3]=-(sqrt(577)-1)/36,y[3]=(sqrt(577)+143)/216,z[3]=(sqrt(577)+143)/216]]
x[3]=x[3]


What I expected is:
x[1]=1/2
x[2]=(sqrt(129)+1)/16
x[3]=sqrt(577)+1)/36
But the list "x" does not contain any x-elements of solve and I don't know why.

I would be happy for any help.

Thanks
Sara