\(\hept{\begin{cases}x-y=m\left(1\right)\Rightarrow y=x-m\\2x+y=4\left(2\right)\end{cases}}\)
Thay vào (2) => 2x+(x-m)=4
\(\Leftrightarrow\hept{\begin{cases}y=x-m\\3x-m-4=0\end{cases}\Leftrightarrow\hept{\begin{cases}y=x-m\\x=\frac{4+m}{3}\end{cases}\Leftrightarrow}\hept{\begin{cases}x=\frac{4+m}{3}\\y=\frac{4-m}{3}-m=\frac{4-4m}{3}\end{cases}}}\)
\(\hept{\begin{cases}x-y=m\\2x+y=4\end{cases}}\)\(\Leftrightarrow\hept{\begin{cases}x-y+2x+y=m+4\\2x+y=4\end{cases}}\)\(\Leftrightarrow\hept{\begin{cases}3x=m+4\\2x+y=4\end{cases}}\) \(\Leftrightarrow\) \(\hept{\begin{cases}x=\frac{m+4}{3}\\2.\frac{m+4}{3}+y=4\end{cases}}\)\(\Leftrightarrow\hept{\begin{cases}x=\frac{m+4}{3}\\\frac{2m+8}{3}+y=4\end{cases}}\) \(\Leftrightarrow\hept{\begin{cases}x=\frac{m+4}{3}\\y=\frac{4-2m}{3}\end{cases}}\) Vậy hệ pt có nghiệm duy nhất là: \(\left(x;y\right)=\left(\frac{m+4}{3};\frac{4-2m}{3}\right)\)
