Suppose that you're asked to find one quantity A
as a function of some other quantity x;
in a situation like this,
we call x the independent variable
(and every other variable in the problem, including A,
is called a dependent variable).
In this case,
you should set up a system of equations with one more variable than equations.
You won't be able to solve this completely
and find out what A is definitively,
but that's OK;
all that you need to do
is to solve for A
in an equation that still has x in it (but no other variables).
The general strategy is to solve any equation with x in it
for any variable other than x itself
and then substitute that solution into the other equations.
(In other words, find an equation with the independent variable in it,
then solve for a dependent variable, and substitute.)
Eventually, this should leave you
with an equation with only A and x in it;
when you solve that equation for A, you're done.
This is all much clearer with examples,
and while there are some examples in the textbook,
they may make the whole thing seem harder than it has to be.
The textbook generally makes do
with as few equations and variables as possible,
which has the advantage of keeping the thing short,
but at the disadvantage of making each equation hard to find.
So I've done an example where there are many equations and many variables
but each individual equation is very simple and easy to think of.
(This used to be an example in the textbook, but they took it out.)
Check out the video:
Go back to the course homepage.
This web page and the files linked from it
were written by Toby Bartels, last edited on 2025 January 8.
Toby reserves no legal rights to them.
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