I have the following system of 7 equations with 8 unknowns:

{{{1-s^2=p1*(1-r1^2)/(1+r1^2)}}}
{{{2*s*r5/(1+r5^2)=2*p1*r1/(1+r1^2)}}}
{{{1-s^2=p2*(1-r2^2)/(1+r2^2)}}}
{{{2*s*