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 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 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 các hệ phương trình sau bằng cách đặt ẩn số phụ:
a) \(\left\{{}\begin{matrix}\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{4}{5}\\\dfrac{1}{x}-\dfrac{1}{y}=\dfrac{1}{5}\end{matrix}\right.\);
b) \(\left\{{}\begin{matrix}\dfrac{15}{x}-\dfrac{7}{y}=9\\\dfrac{4}{x}+\dfrac{9}{y}=35\end{matrix}\right.\);
c) \(\left\{{}\begin{matrix}\dfrac{1}{x+y}+\dfrac{1}{x-y}=\dfrac{5}{8}\\\dfrac{1}{x+y}-\dfrac{1}{x-y}=-\dfrac{3}{8}\end{matrix}\right.\);
d) \(\left\{{}\begin{matrix}\dfrac{4}{2x-2y}+\dfrac{5}{3x+y}=-2\\\dfrac{3}{3x+y}-\dfrac{5}{2x-3y}=21\end{matrix}\right.\);
e) \(\left\{{}\begin{matrix}\dfrac{7}{x-y+2}-\dfrac{5}{x+y-1}=4,5\\\dfrac{3}{x-y+2}+\dfrac{2}{x+y-1}=4\end{matrix}\right.\).
a) \(\left\{{}\begin{matrix}2x+4=0\\4x+2y=-3\end{matrix}\right.\) c)\(\left\{{}\begin{matrix}\left(x-15\right).\left(y+2\right)=x.y\\\left(x+15\right).\left(y-1\right)=x.y\end{matrix}\right.\)
b)\(\left\{{}\begin{matrix}2x+4=y\\x+2y=-3\end{matrix}\right.\) d) \(\left\{{}\begin{matrix}\frac{1}{x}+\frac{1}{y}=5\\\frac{2}{x}+\frac{5}{y}=7\end{matrix}\right.\) tính bằng phương pháp cộng dại số
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)\(\left\{{}\begin{matrix}x^2+y^2+x+y=2\\\left(x+1\right)^2-\left(y+2\right)^2=0\end{matrix}\right.\)
1.Giải hệ phương trình:
a.\(\left\{{}\begin{matrix}2\sqrt{2}x+y=2\sqrt{2}\\7x-3y=7\end{matrix}\right.\)
b.\(\left\{{}\begin{matrix}7x+y=-\frac{1}{7}\\-\frac{4}{3}x-2y=1\frac{1}{3}\end{matrix}\right.\)
c.\(\left\{{}\begin{matrix}2\sqrt{5}x+3y=\sqrt{2}\\\sqrt{5}x-y=3\sqrt{2}\end{matrix}\right.\)
d.\(\left\{{}\begin{matrix}\frac{2}{x}+\frac{3}{y}=-5\\\frac{3}{x}-\frac{4}{y}=1\end{matrix}\right.\)
e.\(\left\{{}\begin{matrix}-\frac{5}{3x+1}+\frac{7}{2x+1}=\frac{5}{7}\\\frac{1}{3x+1}-\frac{1}{2y-3}=\frac{2}{7}\\\end{matrix}\right.\)
g.\(\left\{{}\begin{matrix}2x^2+5y^2=129\\-3x^2+y^2=13\end{matrix}\right.\)
giải hệ PT sau
\(\left\{{}\begin{matrix}x+2y=1\\-3x-y=-2\end{matrix}\right.\)
\(\left\{{}\begin{matrix}4x-5y=9\\7x+y=6\end{matrix}\right.\)
\(\left\{{}\begin{matrix}8x+2y=13\\x+y=1\end{matrix}\right.\)
\(\left\{{}\begin{matrix}5x-3y=1\\2x+y=7\end{matrix}\right.\)