Use inverse matrices to find the solution of the system of equations.

{x+6y+2z=225x+5y+2z=405x3y5z=13\displaystyle {\left\lbrace\begin{array}{ccccccc} {x}&+&{6}{y}&+&{2}{z}&=&{22}\\-{5}{x}&+&{5}{y}&+&{2}{z}&=&{40}\\{5}{x}&-&{3}{y}&-&{5}{z}&=&-{13}\end{array}\right.}