$\{\begin{array}{l}4x+2y=3\cdot \frac{3}{2}y\\ 3x+21=4y+4\end{array}$

$\{\begin{array}{l}4x=\frac{9}{2}y-2y|\cdot 2\\ 3x+17=4y\end{array}$

$\{\begin{array}{l}8x=9y-4y\\ 3x+17=4y\end{array}$

$\{\begin{array}{l}8x=5y|:8\\ 3x+17=4y\end{array}$

$\{\begin{array}{l}x=\frac{5}{8}y\\ 3\cdot \frac{5}{8}y+17=4y\end{array}$

$\{\begin{array}{l}x=\frac{5}{8}y\\ \frac{15}{8}y+17=4y|\cdot 8\end{array}$

$\{\begin{array}{l}x=\frac{5}{8}y\\ 15y+136=32y|-15y\end{array}$

$\{\begin{array}{l}x=\frac{5}{8}y\\ 136=17y\end{array}$

$\{\begin{array}{l}x=\frac{5}{8}y\\ y=8\end{array}$

$\{\begin{array}{l}x=\frac{5}{8}\cdot 8\\ y=8\end{array}$

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

Odp.: Szukany ułamek to $\frac{5}{8}$.