$$-8x^2 +25wx=9 (\sqrt {25-w^2}) (5-\sqrt {25-x^2})$$; $$8w^2-8y^2+25x(y-x)=9(\sqrt{25-x^2})(\sqrt{25-w^2}-\sqrt{25-y^2})$$; $$25y(z-x)+8x^2-8z^2=9(\sqrt{25-x^2}-\sqrt{25-z^2})$$; $$16y^2+9w^2-9z^2-50zy=18(\sqrt{(25-z^2)(25-y^2)}-5\sqrt{25-w^2} )$$.
Is this system of equations solvable or not?