a) $\left\{\begin{matrix}2x-3y=1 & \\ x+2y=3 & \end{matrix}\right.$

<=> $\left\{\begin{matrix}2x-3y=1 & \\ x=3-2y & \end{matrix}\right.$

<=>  $\left\{\begin{matrix}x=\frac{11}{7} & \\ y=\frac{5}{7} & \end{matrix}\right.$

Vậy hệ trên có nghiệm $\left\{\begin{matrix}x=\frac{11}{7} & \\ y=\frac{5}{7} & \end{matrix}\right.$

b) $\left\{\begin{matrix}3x+4y=5 & \\ 4x-2y=2 & \end{matrix}\right.$

<=> $\left\{\begin{matrix}3x+4y=5 & \\ 8x-4y=4 & \end{matrix}\right.$

<=> $\left\{\begin{matrix}11x=9 & \\ y=\frac{5-3x}{4} & \end{matrix}\right.$

<=> $\left\{\begin{matrix}x=\frac{9}{11} & \\ y=\frac{7}{11} & \end{matrix}\right.$

Vậy hệ đã cho có nghiệm $\left\{\begin{matrix}x=\frac{9}{11} & \\ y=\frac{7}{11} & \end{matrix}\right.$

c) $\left\{\begin{matrix}\frac{2}{3}x+\frac{1}{2}y=\frac{2}{3} & \\ \frac{1}{3}x-\frac{3}{4}y=\frac{1}{2} & \end{matrix}\right.$

<=> $\left\{\begin{matrix}4x+3y=4 & \\ 4x-9y=6 & \end{matrix}\right.$

<=> $\left\{\begin{matrix}12y=-2 & \\ x=\frac{4-3y}{4} & \end{matrix}\right.$

<=> $\left\{\begin{matrix}x=\frac{9}{8} & \\ x=\frac{-1}{6} & \end{matrix}\right.$

Vậy hệ đã cho có nghiệm $\left\{\begin{matrix}x=\frac{9}{8} & \\ x=\frac{-1}{6} & \end{matrix}\right.$

d) $\left\{\begin{matrix}0,3x-0,2y=0,5 & \\ 0,5x+0,4y=1,2 & \end{matrix}\right.$

<=> $\left\{\begin{matrix}3x-2y=5 & \\ 5x+4y=12 & \end{matrix}\right.$

<=> $\left\{\begin{matrix}11x=22 & \\ y=\frac{12-5x}{4} & \end{matrix}\right.$

<=> $\left\{\begin{matrix}x=2 & \\ y=\frac{1}{2} & \end{matrix}\right.$

Vậy hệ đã cho có nghiệm $\left\{\begin{matrix}x=2 & \\ y=\frac{1}{2} & \end{matrix}\right.$