Giải hệ phương trình: \(\left\{\begin{array}{l} \frac{x+y}{5}=\frac{x-y}{3} \\ \frac{x}{4}=\frac{y}{2}+1 \end{array}\right.\).

* Hướng dẫn giải

 \(\begin{array}{l} \text { Ta có }\left\{\begin{array}{l} \frac{x+y}{5}=\frac{x-y}{3} \\ \frac{x}{4}=\frac{y}{2}+1 \end{array} \Leftrightarrow\left\{\begin{array}{l} 3 x+3 y=5 x-5 y \\ x=2 y+4 \end{array} \Leftrightarrow\left\{\begin{array}{l} 2 x=8 y \\ x=2 y+4 \end{array} \Leftrightarrow\left\{\begin{array}{l} x=4 y \\ x=2 y+4 \end{array}\right.\right.\right.\right. \\ \Leftrightarrow\left\{\begin{array}{l} x=4 y \\ 2 y-4=0 \end{array} \Leftrightarrow\left\{\begin{array}{l} y=2 \\ x=8 \end{array}\right.\right. \end{array}\)