Solution of Linear System

Definition

Solution of linear system is defined as sequence of $n$ numbers $s_1,\dots ,s_n$ for which the substitution $x_1=s_1,\dots ,s_n=x_n$ make each equation in the linear system a true statement.

Remark

For example, the linear system

$$\begin{array}{r}5x+y=3\\ 2x-y=4\end{array}$$

has the solution $x=1,y=-2$. These solutions may be written as $(1,-2)$. More generally, the a solution of a linear system in $n$ unknowns can be written as $(s_1,\dots ,s_n)$, which is called an ordered n-tuple.