\(\Leftrightarrow\left\{{}\begin{matrix}2x+3y=-2\\4x+y=1\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=\frac{1}{2}\\y=-1\end{matrix}\right.\)
Vậy hpt có 1 ng0 duy nhất là \(\left(\frac{1}{2};-1\right)\)
Giải hệ phương trình
1. \(\left\{{}\begin{matrix}x^2+y^2+2x+2y=\left(x+2\right)\left(y+2\right)\\\left(\frac{x}{y+2}\right)^2+\left(\frac{y}{x+2}\right)^2=1\end{matrix}\right.\)
2. \(\left\{{}\begin{matrix}x^2-2xy-6=6y+2x\\\frac{3x^2}{y+1}=4-x\end{matrix}\right.\)
3.\(\left\{{}\begin{matrix}x^2-y=y^2-x\\x^2-x=y+3\end{matrix}\right.\)
4.\(\left\{{}\begin{matrix}x+y+\frac{1}{x}+\frac{1}{y}=\frac{9}{2}\\xy+\frac{1}{xy}+\frac{x}{y}+\frac{y}{x}=5\end{matrix}\right.\)
6.\(\left\{{}\begin{matrix}x^3\left(x-y\right)+x^2y^2=1\\x^2\left(xy+3\right)-3xy=3\end{matrix}\right.\)
7.\(\left\{{}\begin{matrix}x^2+3y-6x=0\\9x^2-6xy^2+y^4-3y+9=0\end{matrix}\right.\)
8.\(\left\{{}\begin{matrix}x^2+y^2+xy=1\\x+y-xy=2y^2-x^2\end{matrix}\right.\)
9.\(\left\{{}\begin{matrix}8x^3-y=y^3-2x\\x^2+y^2=x+2y\end{matrix}\right.\)
10.\(\left\{{}\begin{matrix}2x^2-3xy+y^2+x-y=0\\x^2+x+1=y^2\end{matrix}\right.\)
11.\(\left\{{}\begin{matrix}\left(x^2+y^2\right)\left(x+y+2\right)=4\left(y+2\right)\\x^2+y^2+\left(y+2\right)\left(x+y+2\right)=4\left(y+2\right)\end{matrix}\right.\)
12. \(\left\{{}\begin{matrix}x^2+7=4y^2+4y\\x^2+3xy+2y^2+x+y=0\end{matrix}\right.\)
13. \(\left\{{}\begin{matrix}x^2+y^2=5\\x^3+2y^3+\left(x-5\right)^2+\left(y+5\right)^2=55\end{matrix}\right.\)
14. \(\left\{{}\begin{matrix}\frac{1}{x^2}+\frac{1}{y^2}=3+x^2y^2\\\frac{1}{x^3}+\frac{1}{y^3}+3=x^3y^3\end{matrix}\right.\)
15.\(\left\{{}\begin{matrix}x^2+y^2+4x+2y=3\\x^2+7y^2-4xy+6y=13\end{matrix}\right.\)
16. \(\left\{{}\begin{matrix}x^2-5xy+x-5y^2=42\\7xy+6y^2+42=x\end{matrix}\right.\)
17.\(\left\{{}\begin{matrix}x^2+xy+y^2=13\\x^4+x^2y^2+y^4=91\end{matrix}\right.\)
18.\(\left\{{}\begin{matrix}x^2=\left(2-y\right)\left(2+y\right)\\2x^3=\left(x+y\right)\left(4-xy\right)\end{matrix}\right.\)
Đây là các bài hệ trong đề thi chuyên toán mong mọi người giúp vì mình bận quá nên không thể làm hết được ạ
giải HPT
a) \(\left\{{}\begin{matrix}\left(x+3\right)\left(y-5\right)=xy\\\left(2x-y\right)\left(y+15\right)=2xy\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}\sqrt{4x}-3y+4z^2=-2\\\sqrt{3x}+2y-3z^2=1\\-3\sqrt{x}+y+2z^2=4\end{matrix}\right.\)
\(\left\{{}\begin{matrix}x^3y\left(1+y\right)+x^2y^2\left(2+y\right)+xy^3=30\\x^2y+x\left(1+y+y^2\right)+y=11\end{matrix}\right.\)
giai hpt
a.\(\left\{{}\begin{matrix}x-2\left(y-1\right)=3x\\3x-2\left(y+1\right)=3\left(x-1\right)\end{matrix}\right.\)
b.\(\left\{{}\begin{matrix}3\left(x+1\right)-2y=5-y\\4x-2\left(y+1\right)=-3\end{matrix}\right.\)
Giải hpt : a) \(\left\{{}\begin{matrix}\left(x^2+y^2\right)\left(x+y+1\right)=25\left(y+1\right)\\x^2+xy+2y^2+x-8y=9\end{matrix}\right.\) b) \(\left\{{}\begin{matrix}x^2+y^2+6xy-\frac{1}{\left(x-y\right)^2}+\frac{9}{8}=0\\2y-\frac{1}{x-y}+\frac{5}{4}=0\end{matrix}\right.\)
c) \(\left\{{}\begin{matrix}\frac{x}{x^2-y}+\frac{5y}{x+y^2}=4\\5x+y+\frac{x^2-5y^2}{xy}=5\end{matrix}\right.\) d) \(\left\{{}\begin{matrix}3xy+y+1=21x\\9x^2y^2+3xy+1=117x^2\end{matrix}\right.\)
e) \(\left\{{}\begin{matrix}x\left(x^2-y^2\right)+x^2=1\sqrt{\left(x-y^2\right)^3}\\76x^2-20y^2+2=\sqrt[3]{4x\left(8x+1\right)}\end{matrix}\right.\)
Giải hệ phương trình:
\(a,\left\{{}\begin{matrix}2x^3+x^2y+2x^2+xy+6=0\\x^2+3x+y=1\end{matrix}\right.\)
\(b,\left\{{}\begin{matrix}x^2=\left(2-y\right)\left(2+y\right)\\2x^3=\left(x+y\right)\left(4-xy\right)\end{matrix}\right.\)
\(c,\left\{{}\begin{matrix}\sqrt[3]{x+2y}=4-x-y\\\sqrt[3]{x+6}+\sqrt{2y}=2\end{matrix}\right.\)
Giải hệ phương trình:
1. \(\left\{{}\begin{matrix}x+3=2\sqrt{\left(3y-x\right)\left(y+1\right)}\\\sqrt{3y-2}-\sqrt{\dfrac{x+5}{2}}=xy-2y-2\end{matrix}\right.\)
2. \(\left\{{}\begin{matrix}\sqrt{2y^2-7y+10-x\left(y+3\right)}+\sqrt{y+1}=x+1\\\sqrt{y+1}+\dfrac{3}{x+1}=x+2y\end{matrix}\right.\)
3. \(\left\{{}\begin{matrix}\sqrt{4x-y}-\sqrt{3y-4x}=1\\2\sqrt{3y-4x}+y\left(5x-y\right)=x\left(4x+y\right)-1\end{matrix}\right.\)
4. \(\left\{{}\begin{matrix}9\sqrt{\dfrac{41}{2}\left(x^2+\dfrac{1}{2x+y}\right)}=3+40x\\x^2+5xy+6y=4y^2+9x+9\end{matrix}\right.\)
5. \(\left\{{}\begin{matrix}\sqrt{xy+\left(x-y\right)\left(\sqrt{xy}-2\right)}+\sqrt{x}=y+\sqrt{y}\\\left(x+1\right)\left[y+\sqrt{xy}+x\left(1-x\right)\right]=4\end{matrix}\right.\)
6. \(\left\{{}\begin{matrix}x^4-x^3+3x^2-4y-1=0\\\sqrt{\dfrac{x^2+4y^2}{2}}+\sqrt{\dfrac{x^2+2xy+4y^2}{3}}=x+2y\end{matrix}\right.\)
7. \(\left\{{}\begin{matrix}x^3-12z^2+48z-64=0\\y^3-12x^2+48x-64=0\\z^3-12y^2+48y-64=0\end{matrix}\right.\)
1, Giải các hệ phương trình sau
a, \(\left\{{}\begin{matrix}\left(x+y\right)^2-2xy=26\\x+y=6\end{matrix}\right.\)
b,\(\left\{{}\begin{matrix}2x^2+x-y=0\\xy+3y-5x=7\end{matrix}\right.\)
c, \(\left\{{}\begin{matrix}\left(x-1\right)^2=1-y\\\left(x^2-y\right)^2=2xy\left(1+x\right)\end{matrix}\right.\)
d, \(\left\{{}\begin{matrix}x^2y+y^2x=2\\x^3+y^3+6=8x^2y^2\end{matrix}\right.\)
giải hệ phương trình:
1, \(\left\{{}\begin{matrix}2y\left(4y^2+3x^2\right)=x^4\left(x^2+3\right)\\2012^x\left(\sqrt{2y-2x+5}-x+1\right)=4024\end{matrix}\right.\)
2, \(\left\{{}\begin{matrix}x^3-2x^2y-15x=6y\left(2x-5-4y\right)\\\frac{x^2}{8y}+\frac{2x}{3}=\sqrt{\frac{x^3}{3y}+\frac{x^2}{4}}-\frac{y}{2}\end{matrix}\right.\)
3, \(\left\{{}\begin{matrix}8\left(x^2+y^2\right)+4xy+\frac{5}{\left(x+y\right)^2}=13\\2x+\frac{1}{x+y}=1\end{matrix}\right.\)
1.\(\left\{{}\begin{matrix}x\left(x-2\right)\left(2x-y\right)=6\\\left(x-3\right)^2+2y=10\end{matrix}\right.\)
2. \(\left\{{}\begin{matrix}\frac{1}{\sqrt{x}}+\sqrt{2-\frac{1}{y}}=2\\\frac{1}{\sqrt{y}}+\sqrt{2-\frac{1}{x}}=2\end{matrix}\right.\)
3. \(\left\{{}\begin{matrix}\left(x+1\right)\left(y+1\right)=8\\x\left(x+1\right)+y\left(y+1\right)+xy=17\end{matrix}\right.\)
