May I know how to find the value of $a$ that satisfies all the conditions given

Question

I am doing this question:
For simultaneous equations: $$ ax - y + z =3$$ $$2ax - y + 3z=7$$ $$3ax - y +5z = b$$
Find a value of 'a' such that there exists a solution for which $x>10^6$, and $ y^2 + z^2 <1$, and the value of b is arbitrary.
In this case, what I do is to set $b=11 $ ,$a \neq 0$. So that the value z can be any thing. Since the question only asks for a solution, could we set the values of z and y be 0. So that we could get$$ ax=3$$Thus, $$\frac{3}{a}>10^6$$ $$a<\frac{3}{10^6}$$. Then, we just pick a value of a between 0 and $\frac{3}{10^6}$. May I know whether my working is right, and is there any good way to do this question.
Thank you very much users.