\(\left\{{}\begin{matrix}5x-4y=5\\4x+3y=4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}5x-4y=5\\4x=4-3y\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}5x-4y=5\\x=1-\dfrac{3}{4}y\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}5\left(1-\dfrac{3}{4}y\right)-4y=5\\x=1-\dfrac{3}{4}y\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}5-\dfrac{15}{4}y-4y=5\\x=1-\dfrac{3}{4}y\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}5+\dfrac{1}{4}y=5\\x=1-\dfrac{3}{4}y\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{1}{4}y=0\\x=1-\dfrac{3}{4}y\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=0\\x=1-\dfrac{3}{4}\times0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=0\end{matrix}\right.\)
Vậy hệ phương trình có nghiệm duy nhất là: \(\left(1;0\right)\)
