Least-squares solution to almost-linear equations with a few cross-terms

Question

I have an intermediate number of equations N (say, 15) that I'd like to solve in a least-squares manner for M unknowns (M

To clarify, I have a set up with unknowns $x_i$like:
$y_1 = a_1 x_1 + b_1 x_3$
$y_2 = a_2 x_2 + b_2 x_3$
and so on.

A small percentage of the equations are of the format
$y_9 = a_9 x_9 + b_9 x_5 + c_9 x_1 x_2$

Thanks!