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

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

$6+2y+y=3$

$y=-1,x=4$

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

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

$3\cdot \left(5+y\right)+4y=8$

$15+7y=8$

$y=-1x=4$

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

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

$2\cdot \left(5y-6\right)-3y=-5$  

  $7y-12=-5$  

$7y=7\to y=1x=-1$  

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

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

$y-1+\frac{1}{2}y-2=0$  

$1\frac{1}{2}y=3\to y=2x=1$  

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

$\{\begin{array}{l}y=2x-3\\ 3x+6y=12\end{array}$  

$3x+6\cdot \left(2x-3\right)=12$  

 

$15x-18=12$  

$15x=30\to x=2y=1$

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

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

$3\cdot \left(9+3,5y\right)-4y=14$  

$27+6,5y=14$  

$6,5y=-13\to y=-2x=2$