\(1+3xy=3x+y\Leftrightarrow3x\left(y-1\right)-\left(y-1\right)=0\)
\(\Leftrightarrow\left(3x-1\right)\left(y-1\right)=0\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{3}\\y=1\end{matrix}\right.\)
- Với \(x=\dfrac{1}{3}\) thay vào pt dưới được:
\(y^2=1-x^2=\dfrac{8}{9}\Rightarrow y=\pm\dfrac{2\sqrt{2}}{3}\)
- Với \(y=1\) thay vào pt dưới được:
\(x^2=1-y^2=0\Rightarrow x=0\)
giải hệ pt:
(1) \(\left\{{}\begin{matrix}x^2-3xy+2y^2=0\\3x+y=6\end{matrix}\right.\)
(2)\(\left\{{}\begin{matrix}\dfrac{x-1}{2x+1}-\dfrac{y-2}{y+2}=1\\\dfrac{3x-3}{2x+1}+\dfrac{2y-4}{y+2}=3\end{matrix}\right.\)
(3)\(\left\{{}\begin{matrix}2\left(x+y\right)+\sqrt{x+1}=4\\x+y-3\sqrt{x+1}=-5\end{matrix}\right.\)
Giải hệ pt:
\(\left\{{}\begin{matrix}x+y+1=3xy\\\left(\dfrac{x}{y+1}\right)^2+\left(\dfrac{y}{x+1}\right)^2=\dfrac{1}{2}\end{matrix}\right.\)
giải hệ pt\(\left\{{}\begin{matrix}x^3+y^3-3xy=-1\\x^2y+y^2x+x^2+y^2=4\end{matrix}\right.\)
Giải hệ pt
a) \(\left\{{}\begin{matrix}x^3+6x^2y=7\\2y^3+3xy^2=5\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}6x-xy-2=0\\2\sqrt{\left(x+2\right)\left(3x-y\right)}=y+6\end{matrix}\right.\)
Giải hệ pt:
\(\left\{{}\begin{matrix}x^3+y^3+3xy=1\\\sqrt{\left(4-x\right)\left(13-y\right)}=\dfrac{2x+2y+25}{2x+y+2}\end{matrix}\right.\)
Giải hệ pt
a) \(\left\{{}\begin{matrix}x^2-4xy+y^2=1\\y^2-3xy=4\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}2x^2-3xy+y^2=3\\x^2+2xy-2y^2=6\end{matrix}\right.\)
Giải hệ phương trình : \(\left\{{}\begin{matrix}x^2+y^2+x+y=8\\2x^2+y^2-3xy+3x-2y+1=0\end{matrix}\right.\)
Giải hệ pt:
\(\left\{{}\begin{matrix}x^2+2y^2+3xy+3=0\\\dfrac{x-y+18}{\left(x+y\right)^2}=9\sqrt{x-y}\end{matrix}\right.\)
Giải hệ pt
\(\left\{{}\begin{matrix}\frac{x^2}{\left(y+1\right)^2}+\frac{y^2}{\left(x+1\right)^2}=\frac{1}{2}\\3xy=x+y+1\end{matrix}\right.\)
