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In order to model the complete two-compartment system, we must be able
to solve equation (4). In section
2.2,
we solved the equation by multiplying by two different weights and
then dividing, and we can take a similar approach with the full
two-compartment equation. We can weight equation (4)
with three different weights and then integrate:
By multiplying equation (7) by 
and equation (9) by 
, and then
subtracting the two, we may eliminate the 
term. A similar
operation can be performed on equation (8) and
equation (9). This leaves two equations that do
not contain 
. They may then be divided to produce:
The 
term cancels out of both the numerator and denominator of
equation (10), leaving an equation that only involves
. As with the equation in section 2.2,
this is very difficult to solve for 
. Therefore, a look-up
table was again used. Once the table matching values of 
with
values of the right hand side of equation (10) has been
created, we may evaluate 
through simple lookup. With the
data computed, finding 
is simply a matter of
evaluating either the numerator or denominator of equation
(10) without cancelling 
. With both 
and
known, we may find 
by evaluating equation
(4).