Question

Giải hệ phương trình\(\left\{{}\begin{matrix}x-y=4\\3x+4y=19\end{matrix}\right.\)

Answer 1

\(\left\{{}\begin{matrix}x-y=4\\3x+4y=19\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}3x-3y=12\\3x+4y=19\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x-y=4\\3x-3y-3x-4y=12-19=-7\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=y+4\\-7y=-7\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=5\\y=1\end{matrix}\right.\)

\(Vậy:\left(x,y\right)=\left(5,1\right)\)

Answer 2

\(\left\{{}\begin{matrix}x-y=4\\3x+4y=19\end{matrix}\right.\)\(\Leftrightarrow\)\(\left\{{}\begin{matrix}4x-4y=16\\3x+4y=19\end{matrix}\right.\)\(\Leftrightarrow\)\(\left\{{}\begin{matrix}7x=35\\x-y=4\end{matrix}\right.\)\(\Leftrightarrow\)\(\left\{{}\begin{matrix}x=5\\y=1\end{matrix}\right.\)

Answer 3

bấm máy tính cũng ra mà :))

 

Answer 4

Ta có: \(\left\{{}\begin{matrix}x-y=4\\3x+4y=19\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}3x-3y=12\\3x+4y=19\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-7y=-7\\x-y=4\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}y=1\\x=4+y=4+1=5\end{matrix}\right.\)

Vậy: Hệ phương trình có nghiệm duy nhất là (x,y)=(5;1)