Originally Posted by prime_66
is an under-determined system, so there will be
a free parameter in any solution. So we choose
so that it maximises the convenience of solving
the system in terms of it.
The constant on the RHS of the second equation is , as is the
coefficient of on the LHS. So setting allows
us to divide through by , and solve for in terms of .
Having found and in terms of
we just substitute these into the first equation to solve for
in terms of .