$a)\{\begin{array}{l}x+y=3\\ x-2y=6\end{array}$

$\{\begin{array}{l}x+y=3\\ x=6+2y\end{array}$  

$\{\begin{array}{l}6+2y+y=3\\ x=6+2y\end{array}$

  $\{\begin{array}{l}6+3y=3\\ x=6+2y\end{array}$

$\{\begin{array}{l}3y=3-6\\ x=6+2y\end{array}$

$\{\begin{array}{l}3y=-3\mid :3\\ x=6+2y\end{array}$

$\{\begin{array}{l}y=-1\\ x=6+2y\end{array}$

$\{\begin{array}{l}y=-1\\ x=6+2\cdot \left(-1\right)\end{array}$

$\{\begin{array}{l}y=-1\\ x=6+\left(-2\right)\end{array}$

$\{\begin{array}{l}y=-1\\ x=4\end{array}$

$b)\{\begin{array}{l}x-y=5\\ 3x+4y=8\end{array}$ $b)\{\begin{array}{l}x-y=5\\ 3x+4y=8\end{array}$

$\{\begin{array}{l}x=5+y\\ 3x+4y=8\end{array}$  

$\{\begin{array}{l}x=5+y\\ 3\cdot \left(5+y\right)+4y=8\end{array}$

$\{\begin{array}{l}x=5+y\\ 15+3y+4y=8\end{array}$

$\{\begin{array}{l}x=5+y\\ 15+7y=8\end{array}$

$\{\begin{array}{l}x=5+y\\ 7y=8-15\end{array}$

$\{\begin{array}{l}x=5+y\\ 7y=-7\mid :7\end{array}$

$\{\begin{array}{l}x=5+y\\ y=-1\end{array}$

$\{\begin{array}{l}x=5+\left(-1\right)\\ y=-1\end{array}$

$\{\begin{array}{l}x=4\\ y=-1\end{array}$

$c)\{\begin{array}{l}2x-3y=-5\\ -x+5y=6\end{array}$

$\{\begin{array}{l}2x-3y=-5\\ x=5y-6\end{array}$

  $\{\begin{array}{l}2\cdot \left(5y-6\right)-3y=-5\\ x=5y-6\end{array}$

$\{\begin{array}{l}10y-12-3y=-5\\ x=5y-6\end{array}$   

$\{\begin{array}{l}7y-12=-5\\ x=5y-6\end{array}$  

$\{\begin{array}{l}7y=-5+12\\ x=5y-6\end{array}$  

$\{\begin{array}{l}7y=7\mid :7\\ x=5y-6\end{array}$  

$\{\begin{array}{l}y=1\\ x=5y-6\end{array}$  

$\{\begin{array}{l}y=1\\ x=5-6\end{array}$  

$\{\begin{array}{l}y=1\\ x=-1\end{array}$  

$d)\{\begin{array}{l}3x-3y+3=0\\ x+\frac{1}{2}y-2=0\end{array}$

  $\{\begin{array}{l}x=y-1\\ x+\frac{1}{2}y-2=0\end{array}$  

  $\{\begin{array}{l}x=y-1\\ y-1+\frac{1}{2}y-2=0\end{array}$

$\{\begin{array}{l}x=y-1\\ 1\frac{1}{2}y-3=0\end{array}$  

$\{\begin{array}{l}x=y-1\\ 1\frac{1}{2}y=3\end{array}$  

$\{\begin{array}{l}x=y-1\\ 1\frac{1}{2}y=3\mid :1\frac{1}{2}\end{array}$

$\{\begin{array}{l}x=2-1\\ y=2\end{array}$

$\{\begin{array}{l}x=1\\ y=2\end{array}$  

$e)\{\begin{array}{l}4x-2y=6\mid :2\\ 3x+6y=12\mid :3\end{array}$

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

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

$\{\begin{array}{l}y=2x-3\\ x+2\cdot \left(2x-3\right)=4\end{array}$  

$\{\begin{array}{l}y=2x-3\\ x+4x-6=4\end{array}$  

$\{\begin{array}{l}y=2x-3\\ 5x=4+6\end{array}$

$\{\begin{array}{l}y=2x-3\\ 5x=10\mid :2\end{array}$  

$\{\begin{array}{l}y=2\cdot 2-3\\ x=2\end{array}$  

$\{\begin{array}{l}y=4-3\\ x=2\end{array}$  

$\{\begin{array}{l}y=1\\ x=2\end{array}$  

$f)\{\begin{array}{l}3x-4y=14\\ -2x+7y=-18\end{array}$

$\{\begin{array}{l}3x-4y=14\\ -2x=-18-7y\mid :\left(-2\right)\end{array}$

$\{\begin{array}{l}3x-4y=14\\ x=9+3\frac{1}{2}y\end{array}$  

$\{\begin{array}{l}3\cdot \left(9+3\frac{1}{2}y\right)-4y=14\\ x=9+3\frac{1}{2}y\end{array}$  

$\{\begin{array}{l}27+10\frac{1}{2}y-4y=14\\ x=9+3\frac{1}{2}y\end{array}$  

$\{\begin{array}{l}6\frac{1}{2}y=14-27\\ x=9+3\frac{1}{2}y\end{array}$  

$\{\begin{array}{l}6\frac{1}{2}y=-13\mid :6\frac{1}{2}\\ x=9+3\frac{1}{2}y\end{array}$  

$\{\begin{array}{l}y=-2\\ x=9+3\frac{1}{2}\cdot \left(-2\right)\end{array}$  

$\{\begin{array}{l}y=-2\\ x=9+\left(-7\right)\end{array}$  

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