Biến đổi pt dưới:
\(x^2-4x+4+y\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)^2+y\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2+y\right)\left(x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=2-y\end{matrix}\right.\)
Thay vào pt đầu giải bt
Giải hệ phương trình sau bằng phương pháp thế
1) \(\left\{{}\begin{matrix}x-2y=4\\-2x+5y=-3\end{matrix}\right.\)
2) \(\left\{{}\begin{matrix}2x+y=10\\5x-3y=3\end{matrix}\right.\)
3) \(\left\{{}\begin{matrix}x+2y=4\\-3x+y=7\end{matrix}\right.\)
Giải hệ phương trình sau bằng phương pháp thế
a)
\(\left\{{}\begin{matrix}\sqrt{5}+2)x+y=3-\sqrt{5}\\-x+2y=6-2\sqrt{5}\end{matrix}\right.\)
b)
\(\left\{{}\begin{matrix}5\left(x+2y\right)=3x-1\\2x+4=3\left(x-5y\right)-12\end{matrix}\right.\)
giải các hệ phương trình sau:
\(\left\{{}\begin{matrix}2x+\dfrac{Y}{\sqrt{4X^{2^{ }}+1}+2X}+Y^{2^{ }}=0\\4\left(\dfrac{X}{Y}\right)^{2^{ }}+2\sqrt{4X^{2^{ }}+1}+Y^{2^{ }}=3\end{matrix}\right.\)
\(\left\{{}\begin{matrix}x+y+z=6\\xy+yz+zx=11\\xyz=6\end{matrix}\right.\)
\(\left\{{}\begin{matrix}x^{3^{ }}-y^{3^{ }}-15y-14=3\left(2y^{2^{ }}-x\right)\\4x^{3^{ }}+6xy+15x+3=0\end{matrix}\right.\)
Giải hpt
a)\(\left\{{}\begin{matrix}x+y+z=1\\x+2y+4z=8\\x+3y+9z=27\end{matrix}\right.\) b)\(\left\{{}\begin{matrix}x^2+y^2+x+y=62\\xy=24\end{matrix}\right.\) c)\(\left\{{}\begin{matrix}\dfrac{3}{2x+y}+z=2\\2y-3z=4\\\dfrac{2}{2x+y}-y=\dfrac{3}{2}\end{matrix}\right.\)
Giải hệ phương trình
a)\(\left\{{}\begin{matrix}6x^2-3xy+x=1-y\\x^2+y^2=1\end{matrix}\right.\) c)\(\left\{{}\begin{matrix}\left|x+1\right|+\left|y-1\right|=5\\\left|x+1\right|-4y+4=0\end{matrix}\right.\)
b)\(\left\{{}\begin{matrix}2x^2-2x+xy-y=0\\x^2-3xy+4=0\end{matrix}\right.\)
Giải hệ phương trình
a)\(\left\{{}\begin{matrix}x+y=\dfrac{x-3}{2}\\x+2y=\dfrac{2-4y}{15}\end{matrix}\right.\) b)\(\left\{{}\begin{matrix}\dfrac{1}{x}+\dfrac{1}{y}=-1\\\dfrac{3}{x}-\dfrac{2}{y}=7\end{matrix}\right.\)
c)\(\left\{{}\begin{matrix}\sqrt{x+3}-2\sqrt{y+1}=2\\2\sqrt{x+3}+\sqrt{y+1}=4\end{matrix}\right.\) d)\(\left\{{}\begin{matrix}\dfrac{7}{\sqrt{x}-7}-\dfrac{4}{\sqrt{y}+6}=\dfrac{5}{3}\\\dfrac{5}{\sqrt{x}-7}+\dfrac{3}{\sqrt{y}+6}=2\dfrac{1}{9}\end{matrix}\right.\)
1)\(\left\{{}\begin{matrix}x^2-y^2-2x+2y=0\\x^2-3xy+5y^2-3=0\end{matrix}\right.\)
2)\(\left\{{}\begin{matrix}\frac{1}{x}+\frac{1}{1-y}=1\\\frac{1}{x-1}-\frac{1}{y}=2\end{matrix}\right.\)
3)\(\left\{{}\begin{matrix}x^2-4x+3=0\\x^2+xy+y^2=1\end{matrix}\right.\)
4)\(\left\{{}\begin{matrix}x^2+y^2+x+y=2\\\left(x+1\right)^2-\left(y+2\right)^2=0\end{matrix}\right.\)
Giải hệ phương trình
\(\left\{{}\begin{matrix}4\left(2x-y+3\right)-3\left(x-2y+3\right)=48\\3\left(3x-4y+3\right)+4\left(4x-2y-9\right)=48\end{matrix}\right.\)
\(\left\{{}\begin{matrix}6\left(x+y\right)=8+2x-3y\\5\left(y-x\right)=5+3x+2y\end{matrix}\right.\)
\(\left\{{}\begin{matrix}-2\left(2x+1\right)+1,5=3\left(y-2\right)-6x\\11,5-4\left(3-x\right)=2y-\left(5-x\right)\end{matrix}\right.\)
\(\left\{{}\begin{matrix}\dfrac{8x-5y-3}{7}+\dfrac{11y-4x-7}{5}=12\\\dfrac{9x+4y-13}{5}-\dfrac{3\left(x-2\right)}{4}=15\end{matrix}\right.\)
\(\left\{{}\begin{matrix}2\sqrt{3}x-\sqrt{5}y=2\sqrt{6}-\sqrt{15}\\3x-y=3\sqrt{2}-\sqrt{3}\end{matrix}\right.\)
Giải hệ pt:
\(\left\{{}\begin{matrix}\left(x-1\right)\left(y+3\right)=xy+27\\\left(x-2\right)\left(y+1\right)=xy+8\end{matrix}\right.\)
