Question

Giúp mình câu 3.

Answer 1

3) Ta có hệ phương trình :

\(\left\{{}\begin{matrix}x+y=k+2\\2x+4y=9-k\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2x+2y=2k+4\\2x+4y=9-k\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2x+2y=2k+4\\\left(2x+4y\right)-\left(2x+2y\right)=9-k-\left(2k+4\right)\end{matrix}\right.\)

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

\(\Leftrightarrow\left\{{}\begin{matrix}x=k+2-\dfrac{5-3k}{2}=\dfrac{5k-1}{2}\\y=\dfrac{5-3k}{2}\end{matrix}\right.\)

Vậy hệ phương trình cho có nghiệm \(\left(x,y\right)=\left(\dfrac{5k-1}{2},\dfrac{5-3k}{2}\right)\)