2.4 Equations and Functions

An equation always shows a relationship between variables, but the relationship is not necessarily to be viewed as a function with independent and dependent variables. For example, in the equation $4p+3q=7$, there is no requirement that one variable be independent and the other dependent.

In linear equations it is always possible to solve for any variable shown in the equation -that is, to rewrite the equation with that variable by itself on one side of the equation. If this is done, it is a convention to write the variable on the left-hand side of the equation and treat it as the dependent variable. Thus, in the example above, you could solve for p as follows:

$p = \frac{7}{4}-\frac{3q}{4}$

and treat p as a function of q. Similarly you could solve for q as follows:

$q = \frac{7}{3}-\frac{4p}{3}$

and treat  as a function of p.

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