Question

\(\left\{{}\begin{matrix}2.\left(x+y\right)+3.\left(x-y\right)=4\\\left(x+y\right)+2.\left(x-y\right)=5\end{matrix}\right.\)

Answer 1

\(\left\{{}\begin{matrix}2\left(x+y\right)+3\left(x-y\right)=4\\\left(x+y\right)+2\left(x-y\right)=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2\left(x+y\right)+3\left(x-y\right)=4\\2\left(x+y\right)+4\left(x-y\right)=10\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x-y=6\\\left(x+y\right)+2\left(x-y\right)=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=x-6\\2x-6+12=5\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}y=x-6\\x=-\dfrac{1}{2}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-\dfrac{13}{2}\\x=-\dfrac{1}{2}\end{matrix}\right.\)