The R=1 and x=1 appear to confuse WolframAlpha.
This
solve a+1+g=0, b+y+h=0, c+z+j=0, a^2+b^2+c^2=1, 1+y^2+z^2=1 for real y
WASolve
will have WolframAlpha solve for real values of y and solve for all the other variables at the same time.
