Coefficient Swap

Suppose that we have two datasets $X$ and $Y$ with $\text{Var}(X) = 10$ and $\text{Var}(Y) = 20$. We perform the linear regression $y \sim \alpha_x + \beta_x x$ and obtain $\beta_x = 1$. Suppose now that we perform the regression $x \sim \alpha_y + \beta_y y$. Find $\beta_y$. If the value can't be determined, enter $-100$.