Question

[Nhi Đào Quỳnh]

Giải phương trình

1. \(\hept{\begin{cases}\frac{1}{x}+2\left(x+y\right)=3\\3x\left(x+y\right)-x=2\end{cases}}\)
2. \(\hept{\begin{cases}\frac{x+y}{x-y}+\frac{2x}{y+1}=3\\\frac{x+y}{2\left(x-y\right)}-\frac{3x}{y+1}=\frac{-1}{2}\end{cases}}\)
3. \(\hept{\begin{cases}2x+3y=xy+5\\\frac{1}{x}+\frac{1}{y+1}=1\end{cases}}\)

Answer 1

[Nyatmax]

1.

\(ĐK:x\ne0\)

HPT

\(\Leftrightarrow\hept{\begin{cases}2x\left(x+y\right)-3x+1=0\\3x\left(x+y\right)-x-2=0\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}3x\left(x+y\right)-\frac{9}{2}x+\frac{3}{2}=0\left(1\right)\\3x\left(x+y\right)-x-2=0\left(2\right)\end{cases}}\)

\(\left(1\right)-\left(2\right)\Leftrightarrow\frac{7}{2}x=\frac{7}{2}\)

\(\Leftrightarrow x=1\left(3\right)\)

\(\left(1\right),\left(3\right)\Rightarrow3\left(1+y\right)-3=0\)

\(\Leftrightarrow y=0\)

Vay nghiem cua HPT la \(\left(1;0\right)\)