System of Linear Equations - Elementary Example

Elementary Example

The simplest kind of linear system involves two equations and two variables:

\begin{alignat}{5} 2x &&\; + \;&& 3y &&\; = \;&& 6 & \\ 4x &&\; + \;&& 9y &&\; = \;&& 15&. \end{alignat}

One method for solving such a system is as follows. First, solve the top equation for in terms of :

Now substitute this expression for x into the bottom equation:

This results in a single equation involving only the variable . Solving gives, and substituting this back into the equation for yields . This method generalizes to systems with additional variables (see "elimination of variables" below, or the article on elementary algebra.)

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