The first equation is
$13 b + 4t = 487$
They've solved for $b=23$
Then back solving is taking the value of $b$ and plugging it back into one of the original equations, i.e.
$13(23) + 4t = 487$
and solving for the remaining variable $t$
$299 + 4t = 487$
$4t = 188$
$t = 47$