$a)\{\begin{array}{l}2x+3y=13\\ 3x-2y=0\mid +2y\end{array}$  

$\{\begin{array}{l}2x+3y=13\\ 3x=2y\mid :3\end{array}$

$\{\begin{array}{l}2x+3y=13\\ x=\frac{2}{3}y\end{array}$  

$\{\begin{array}{l}2\cdot \frac{2}{3}y+3y=13\\ x=\frac{2}{3}y\end{array}$  

$\{\begin{array}{l}\frac{4}{3}y+3y=13\\ x=\frac{2}{3}y\end{array}$  

$\{\begin{array}{l}1\frac{1}{3}y+3y=13\\ x=\frac{2}{3}y\end{array}$  

$\{\begin{array}{l}4\frac{1}{3}y=13\\ x=\frac{2}{3}y\end{array}$  

$\{\begin{array}{l}\frac{13}{3}y=13\mid :\frac{13}{3}\\ x=\frac{2}{3}y\end{array}$  

$\{\begin{array}{l}y=13:\frac{13}{3}\\ x=\frac{2}{3}y\end{array}$  

$\{\begin{array}{l}y={\sout{13}}^1\cdot \frac{3}{{\sout{13}}^1}\\ x=\frac{2}{3}y\end{array}$  

$\{\begin{array}{l}y=3\\ x=\frac{2}{{\sout{3}}^2}\cdot {\sout{3}}^1\end{array}$  

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

$b)\{\begin{array}{l}3a+4b=9\\ 2a-3b=-11\mid +3b\end{array}$  

$\{\begin{array}{l}3a+4b=9\\ 2a=-11+3b\mid :2\end{array}$  

$\{\begin{array}{l}3a+4b=9\\ a=\frac{-11+3b}{2}\end{array}$  

$\{\begin{array}{l}3\cdot \frac{-11+3b}{2}+4b=9\\ a=\frac{-11+3b}{2}\end{array}$  

$\{\begin{array}{l}\frac{-33+9b}{2}+4b=9\mid \cdot 2\\ a=\frac{-11+3b}{2}\end{array}$  

$\{\begin{array}{l}-33+9b+8b=18\mid +33\\ a=\frac{-11+3b}{2}\end{array}$  

$\{\begin{array}{l}17b=51\mid :17\\ a=\frac{-11+3b}{2}\end{array}$  

  $\{\begin{array}{l}b=3\\ a=\frac{-11+3\cdot 3}{2}\end{array}$  

$\{\begin{array}{l}b=3\\ a=\frac{-11+9}{2}\end{array}$  

$\{\begin{array}{l}b=3\\ a=-\frac{2}{2}=-1\end{array}$  

$c)\{\begin{array}{l}\frac{2}{3}m-\frac{3}{5}n=-2\mid \cdot 15\\ \frac{5}{6}m+\frac{2}{5}n=9\mid \cdot 30\end{array}$  

$\{\begin{array}{l}{\sout{15}}^5\cdot \frac{2}{{\sout{3}}^1}m-{\sout{15}}^3\cdot \frac{3}{{\sout{5}}^1}n=15\cdot \left(-2\right)\\ {\sout{30}}^5\cdot \frac{5}{{\sout{6}}^1}m+{\sout{30}}^6\cdot \frac{2}{{\sout{5}}^1}n=30\cdot 9\end{array}$  

$\{\begin{array}{l}10m-9n=-30\mid +9n\\ 25m+12n=270\end{array}$  

  $\{\begin{array}{l}10m=-30+9n\mid :10\\ 25m+12n=270\end{array}$  

$\{\begin{array}{l}m=-3+\frac{9}{10}n\\ 25m+12n=270\end{array}$  

$\{\begin{array}{l}m=-3+\frac{9}{10}n\\ 25\cdot \left(-3+\frac{9}{10}n\right)+12n=270\end{array}$  

$\{\begin{array}{l}m=-3+\frac{9}{10}n\\ -75+{\sout{25}}^5\cdot \frac{9}{{\sout{10}}^2}n+12n=270\end{array}$  

$\{\begin{array}{l}m=-3+\frac{9}{10}n\\ -75+\frac{45}{2}n+12n=270\mid +75\end{array}$  

$\{\begin{array}{l}m=-3+\frac{9}{10}n\\ 34,5n=345\mid :34,5\end{array}$  

$\{\begin{array}{l}m=-3+\frac{9}{10}n\\ n=10\end{array}$  

$\{\begin{array}{l}m=-3+\frac{9}{{\sout{10}}^1}\cdot {\sout{10}}^1\\ n=10\end{array}$  

$\{\begin{array}{l}m=-3+9\\ n=10\end{array}$  

$\{\begin{array}{l}m=6\\ n=10\end{array}$