Question

Giải hệ phương trình

X + y = 1

2x - y = 8

Answer 1

\(\left\{{}\begin{matrix}x+y=1\\2x-y=8\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2x+2y=2\\2x-y=8\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x+y=1\\\left(2x-2x\right)+\left(2y+y\right)=2-8\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x+y=1\\3y=-6\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x+y=1\\y=-2\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x-2=1\\y=-2\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=-2\end{matrix}\right.\)

Vậy hệ pt có nghiệm duy nhất \(\left(x;y\right)=\left(3;-2\right)\)