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 :

linsolve([2*x+y+z=1,x+y+2*z=1,x+2*y+z=4],[x,y,z])

Output :

[1/-2,5/2,1/-2]

Which means that

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

is the solution of the system :

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