Least absolute deviations problem minimization

$min_{β∈R}|y_j − x_{j1}β_1|$, for j = 1,….N

Here y is the dependent variable and x is the independent variable. What happens to the case when $x_{j1}=1$ for all j?

If I graph it, it’s a parallel line to the y axis. And β is undefined. So how does the minimization problem works?