Is there any solution to the following system of equations? Is there any solution to the following system of diophantine equations?
$$
\left\{\begin{array}{l} 
2.a^2 = b^2+c^2+d^2 \\
a^2 = e^2+f^2+g^2 , & \mbox{with }((a,b,c,d,e,f,g)>2)\in N\mbox{ and differents among them}
\end{array}
\right.
$$

set of equations:
$\left\{\begin{aligned}&X^2+Y^2+Z^2=2(R^2+W^2)\\&F^2+G^2+T^2=R^2+W^2\end{aligned}\right.$
has solutions
$X=4(t^2+q^2-a^2-v^2)a^2+(v^2+t^2+q^2-z^2)^2$
$Y=4(v^2-a^2-t^2-q^2)a^2+(v^2+t^2+q^2-z^2)^2$
$Z=4az(v^2+t^2+q^2-2a^2-z^2)$
$F=4(a^2+z^2-2t^2-2q^2)a^2+(v^2+t^2+q^2-z^2)^2$
$G=4aq(v^2+t^2+q^2-2a^2-z^2)$
$T=4at(v^2+t^2+q^2-2a^2-z^2)$
$R=4(z^2+a^2-2v^2)a^2+(v^2+t^2+q^2-z^2)^2$
$W=4av(v^2+t^2+q^2-2a^2-z^2)$
$a,v,t,q,z$ - integers and sets us.
