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Linear system solving: linsolve

linsolve is used to solve a system of linear equations.
linsolve has two arguments: a list of equations or expressions (in that case the convention is that the equation is expression = 0), and a list of variable names.
linsolve returns the solution of the system in a list.
Input :
Output :
Which means that

x = - $\displaystyle {\frac{{1}}{{2}}}$, y = $\displaystyle {\frac{{5}}{{2}}}$, z = - $\displaystyle {\frac{{1}}{{2}}}$

is the solution of the system :

$\displaystyle \left\{\vphantom{
2x+y+z &=1\\
x+y+2z &=1\\
x+2y+z &=4
\end{array}}\right.$$\displaystyle \begin{array}{rl}
2x+y+z &=1\\
x+y+2z &=1\\
x+2y+z &=4

giac documentation written by Renée De Graeve and Bernard Parisse