#[Examples][Ejemplos]#
1. #[The reduced matrix][La matiz reducida]# #[represents the system of equations][representa el sistema de ecuaciones]# #[and so a unique solution][y así una solución]# $(x, y) = (9, -6)$.

2. #[The matrix][La matiz]# #[represents the system of equations][representa el sistema de ecuaciones]# #[Ignoring the second equation (which tells us nothing interesting) and solving the first equation for $x$ gives][Ignorando la segunda ecuación (que no nos dice nada interesante), obtenemos, resolviendo $x$ en la primera ecuación nos da]# This tells us that, so long as $x$ satisfies this equation, the system of equations is satisfied regardless of the value of $y$; for instance, if we choose $y = 100$ we get $x = 3(100)+4 = 304$, and therefore the solution $(x, y) = (304, 100)$. But this is only one particular solution. We can get other particular solutions by choosing other values for $y$, such as $y = 0$, which gives us another particular solution: $(x, y) = (4, 0)$.

To represent all possible solutions, we don't specify any particular value for $y$, and just write #[This is called the general solution because every particular solution can be obtained from the general solution by choosing a value for the arbitrary varaiable $y$. For instance, choosing $y=-1$ gives us a particular solution][Esto se denomina solución general porque cualquier solución particular se puede obtener a partir de la solución general eligiendo un valor para la variable arbitraria $y$. Por ejemplo, si elegimos $y=-1$, obtenemos una solución particular.]#

#[Alternative way to write the general solution][Una manera alternativa escribir la solución general.]#
#[We can get another way of writing the general solution by solving for $y$ instead of $x$][]# #[where this time $x$ is arbitrary][donde esta vez $x$ es arbitraria]#: