`{(2\sqrt{5x-1}-5/[|y+3|]=-1),(3\sqrt{5x-1}+7/[|y+3|]=13):}` `ĐK: x >= 1/5;y ne -3`
Đặt `\sqrt{5x-1}=a;1/[|y+3|]=b` khi đó ta có:
`{(2a-5b=-1),(3a+7b=13):}`
`<=>{(6a-15b=-3),(6a+14b=26):}`
`<=>{(29b=29),(2a-5b=-1):}`
`<=>{(b=1),(2a-5.1=-1):}`
`<=>{(a=2),(b=1):}`
`=>{(\sqrt{5x-1}=2),(1/[|y+3|]=1):}`
`<=>{(5x-1=2),([(y+3=1),(y+3=-1):}):}`
`<=>{(x=3/5),([(y=-2),(y=-4):}):}` (t/m)
giải hệ phương trình sau : \(\left\{{}\begin{matrix}\sqrt{2x+1}+\dfrac{2}{\left|y+3\right|}=3\\2\sqrt{2x+1}+\dfrac{3}{4\left|y+3\right|}=5\end{matrix}\right.\)
Giải hệ phương trình
\(\left\{{}\begin{matrix}\dfrac{1}{\sqrt{2x-1}}+\dfrac{5}{\sqrt{3-y}}=7\\\dfrac{3}{\sqrt{2x-1}}-\dfrac{7}{\sqrt{3-y}}=-1\end{matrix}\right.\)
Giải hệ phương trình sau:
a. \(\left\{{}\begin{matrix}\dfrac{x+2}{y}=\dfrac{x+1}{y-2}\\\dfrac{5x+1}{5x-2}=\dfrac{y-2}{y+2}\end{matrix}\right.\)
b. \(\left\{{}\begin{matrix}2x+\left|y\right|=4\\4x-3y=1\end{matrix}\right.\)
Giải các hệ phương trình sau bằng phương pháp thế:
a)\(\left\{{}\begin{matrix}3x-2y=11\\4x-5y=3\end{matrix}\right.\)
b)\(\left\{{}\begin{matrix}\dfrac{x}{2}-\dfrac{y}{3}=1\\5x-8y=3\end{matrix}\right.\)
c)\(\left\{{}\begin{matrix}3x+5y=1\\2x-y=-8\end{matrix}\right.\)
d)\(\left\{{}\begin{matrix}\dfrac{x}{y}=\dfrac{2}{3}\\x+y-10=0\end{matrix}\right.\)
Giải hệ phương trình :
\(\left\{{}\begin{matrix}3\sqrt{x-3}-\dfrac{1}{y+1}=1\\\sqrt{x-3}+\dfrac{2}{y+1}=5\end{matrix}\right.\)
Giải hpt:
a)\(\left\{{}\begin{matrix}\dfrac{2y-5x}{3}+5=\dfrac{y+27}{4}-2x\\\dfrac{x+1}{3}+y=\dfrac{6y-5x}{7}\end{matrix}\right.\)
b)\(\left\{{}\begin{matrix}\dfrac{1}{2}\left(x+2\right)\left(y+3\right)-\dfrac{1}{2}xy=50\\\dfrac{1}{2}xy-\dfrac{1}{2}\left(x-2\right)\left(y-2\right)=32\end{matrix}\right.\)
c)\(\left\{{}\begin{matrix}\left(x+20\right)\left(y-1\right)=xy\\\left(x-10\right)\left(y+1\right)=xy\end{matrix}\right.\)
d)\(\left\{{}\begin{matrix}\dfrac{2}{x+2y}+\dfrac{1}{y+2x}=3\\\dfrac{4}{x+2y}-\dfrac{3}{y+2x}=1\end{matrix}\right.\)
e)\(\left\{{}\begin{matrix}\dfrac{3x}{x+1}-\dfrac{2}{y+4}=4\\\dfrac{2x}{x+1}-\dfrac{5}{y+4}=9\end{matrix}\right.\)
Giải hệ phương trình: \(\left\{{}\begin{matrix}\dfrac{3}{\sqrt[]{x+y}}-\dfrac{2}{\sqrt[]{x-y}}=4\\\dfrac{2}{\sqrt[]{x+y}}+\dfrac{1}{\sqrt[]{x-y}}=5\end{matrix}\right.\)
Giải hệ phương trình sau
\(\left\{{}\begin{matrix}\sqrt{x+1}+\sqrt{4-2y}+\sqrt{5+2y-\left(x-1\right)^2}\\5x^4+\left(x-y\right)^2=\left(10x^3+y\right)y\end{matrix}\right.\)
Giải hệ bằng phương pháp phân tích nhân tử
a) \(\left\{{}\begin{matrix}\dfrac{1}{x^2}+\dfrac{1}{y^2}=1\\\sqrt{x^2-1}+\sqrt{y^2-1}=\sqrt{xy+2}\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}\left(x-y\right)\left(x^2+y^2\right)=13\\\left(x+y\right)\left(x^2-y^2\right)=25\end{matrix}\right.\)
