Question

giải hệ phương trình

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

Answer 1

`{(-2x+y=2),(2x-2y=1):}`

`<=>{(-4x+2y=4),(2x-2y=1):}`

`<=>{(-2x=5),(-2x+y=2):}`

`<=>{(x=[-5]/2),(-2 . [-5]/2+y=2):}`

`<=>{(x=[-5]/2),(y=-3):}`

Vậy hệ ptr có nghiệm `(x;y)=([-5]/2;-3)`

Answer 2

\(\left\{{}\begin{matrix}-2x+y=2\\2x-2y=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=2+2x\\2x-4-4x=1\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}y=2\left(1+x\right)\\-2x-4=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=2\left(x+1\right)\\-2x=5\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}y=2\left(-\dfrac{5}{2}+1\right)\\x=-\dfrac{5}{2}\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}y=-3\\x=-\dfrac{5}{2}\end{matrix}\right.\)