a) Sử dụng định lí 1, ta được

- Hướng dẫn giải

a) Sử dụng định lí 1, ta được $\left\{\begin{array}{c}\mathrm{x}+3\mathrm{y}=2\\ 3\mathrm{x}+8\mathrm{y}=5\end{array}\right.\iff \left\{\begin{array}{c}\frac{1}{2}\mathrm{x}+\frac{3}{2}\mathrm{y}=1\\ 3\mathrm{x}+8\mathrm{y}=5\end{array}\right.$

Sử dụng định lí 2, ta được

$$\begin{gathered} \left\{\begin{array}{c}\mathrm{x}+3\mathrm{y}=2\\ 3\mathrm{x}+8\mathrm{y}=5\end{array}\right. \\ \iff \left\{\begin{array}{c}\mathrm{x}+3\mathrm{y}=2\\ \left(3\mathrm{x}+8\mathrm{y}\right)-\left(\mathrm{x}+3\mathrm{y}\right)=5-2\end{array}\right. \\ \iff \left\{\begin{array}{c}\mathrm{x}+3\mathrm{y}=2\\ 2\mathrm{x}+5\mathrm{y}=3\end{array}\right. \end{gathered}$$

Sử dụng định lí 3, ta được

$$\begin{gathered} \left\{\begin{array}{c}\mathrm{x}+3\mathrm{y}=2\\ 3\mathrm{x}+8\mathrm{y}=5\end{array}\right.\iff \left\{\begin{array}{c}\mathrm{x}=2-3\mathrm{y}\\ 3\left(2-3\mathrm{y}\right)+8\mathrm{y}=5\end{array}\right. \\ \iff \left\{\begin{array}{c}\mathrm{x}=2-3\mathrm{y}\\ -9\mathrm{y}+8\mathrm{y}=-1\end{array}\right. \end{gathered}$$

b) Sử dụng định lí 1, ta được $\left\{\begin{array}{c}\mathrm{x}+\mathrm{y}=7\\ 3\mathrm{x}+4\mathrm{y}=25\end{array}\right.\iff \left\{\begin{array}{c}\frac{\mathrm{x}}{7}+\frac{\mathrm{y}}{7}=1\\ 3\mathrm{x}+4\mathrm{y}=25\end{array}\right.$

Sử dụng định lí 2, ta được

$$\begin{gathered} \left\{\begin{array}{c}\mathrm{x}+\mathrm{y}=7\\ 3\mathrm{x}+4\mathrm{y}=25\end{array}\right. \\ \iff \left\{\begin{array}{c}\mathrm{x}+\mathrm{y}=7\\ \left(3\mathrm{x}+4\mathrm{y}\right)-\left(\mathrm{x}+\mathrm{y}\right)=25-7\end{array}\right. \\ \iff \left\{\begin{array}{c}\mathrm{x}+\mathrm{y}=7\\ 2\mathrm{x}+3\mathrm{y}=18\end{array}\right. \end{gathered}$$

Sử dụng định lí 3, ta được

$$\begin{gathered} \left\{\begin{array}{c}\mathrm{x}+\mathrm{y}=7\\ 3\mathrm{x}+4\mathrm{y}=25\end{array}\right.\iff \left\{\begin{array}{c}\mathrm{x}=7-\mathrm{y}\\ 3\left(7-\mathrm{y}\right)+4\mathrm{y}=25\end{array}\right. \\ \iff \left\{\begin{array}{c}\mathrm{x}=7-\mathrm{y}\\ \mathrm{y}=4\end{array}\right. \end{gathered}$$