$a)\{\begin{array}{l}6x+y=22\mid -6x\\ x-2y=8\end{array}$  

$\{\begin{array}{l}y=22-6x\\ x-2\cdot \left(22-6x\right)=8\end{array}$  

$\{\begin{array}{l}y=22-6x\\ x-44+12x=8\end{array}$  

$\{\begin{array}{l}y=22-6x\\ 13x-44=8\mid +44\end{array}$  

$\{\begin{array}{l}y=22-6x\\ 13x=52\mid :13\end{array}$  

$\{\begin{array}{l}y=22-6x\\ x=4\end{array}$  

$\{\begin{array}{l}y=22-6\cdot 4\\ x=4\end{array}$  

$\{\begin{array}{l}y=22-24=-2\\ x=4\end{array}$  

  $b)\{\begin{array}{l}6x+y=22\\ x-2y=8\mid +2y\end{array}$  

$\{\begin{array}{l}6x+y=22\\ x=8+2y\end{array}$  

$\{\begin{array}{l}6\cdot \left(8+2y\right)+y=22\\ x=8+2y\end{array}$  

$\{\begin{array}{l}48+12y+y=22\mid -48\\ x=8+2y\end{array}$   

$\{\begin{array}{l}13y=-26\\ x=8+2y\end{array}$  

$\{\begin{array}{l}y=-2\\ x=8+2\cdot \left(-2\right)\end{array}$  

$\{\begin{array}{l}y=-2\\ x=8+\left(-4\right)\end{array}$  

$\{\begin{array}{l}y=-2\\ x=4\end{array}$