kill(all)$

van=facebook.com/LearningCalculus$

f(x,y,z):=x^2-y*z=1$
g(x,y,z):=y^2-x*z=4$
h(x,y,z):=z^2-x*y=9$
F(x,y,z):=[f(x,y,z),g(x,y,z),h(x,y,z)]$ F(x,y,z);
U(x,y,z):=[x,y,z]$

F(-1,0,3);

solve(f(x,y,z),x);
solve(g(x,y,z),x);
solve(h(x,y,z),x);

solve(f(x,y,z),y);
solve(g(x,y,z),y);
solve(h(x,y,z),y);

solve(f(x,y,z),z);
solve(g(x,y,z),z);
solve(h(x,y,z),z);