Linear combination of random variables: equation for a coefficient

$W$ is a random variable such that $W = aX + bY$, where $X$ and $Y$ are independent random variables and $a, b \in \R$.

Given that $\operatorname{E}(X) = 1$, $\operatorname{Var}(X) = 1$, $\operatorname{E}(Y) = 2$, $\operatorname{Var}(Y) = 2$, $E(W) = 1$ and $\operatorname{Var}(W) = 6$, then $b$ satisfies