Solving Simple Equations

Understanding Variables

To a mathematician or an economist, a variable is the name given to a quantity that can assume a range of values. In other words, the value of a variable can change or vary. In an equation it’s represented by a letter or a symbol. Because economic models often consider cause and effect, variables are important. You will often be asked to consider a range of options that result from different variables. Below is a very simple example:

$y=9+3x$

In order to understand the range of options, we might start with 0. What does y equal if $\displaystyle x=0$?

$\displaystyle \begin{array}{l}y=9+3x\\y=9+3(0)\\y=9+0\\y=9\end{array}$

Now, let’s look at the same formula with different information. What does y equal if $\displaystyle x=5$?

$\displaystyle \begin{array}{l}y=9+3x\\y=9+3(5)\\y=9+15\\y=24\end{array}$