Question

15) \(\left\{{}\begin{matrix}3x+2y=7\\x^2+y^2-7x+xy=0\end{matrix}\right.\)

16)\(\left\{{}\begin{matrix}2x+3y=5\\x^2+xy+y^2-4x=-1\end{matrix}\right.\)

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Answer 1

\(\left\{{}\begin{matrix}3x+2y=7\\x^2+y^2-7x+xy=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x+2y=7\\x^2+y^2-3x^2-2xy+xy=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}3x+2y=7\\-2x^2-xy+y^2=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}3x+2y=7\\-\left(x+y\right)\left(2x-y\right)=0\end{matrix}\right.\)

TH1: \(\left\{{}\begin{matrix}3x+2y=7\\x+y=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=7\\y=-7\end{matrix}\right.\)

TH2: \(\left\{{}\begin{matrix}3x+2y=7\\2x-y=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=2\end{matrix}\right.\)

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