Question

Rezolvați următoarele sisteme de ecuații:
va rog!!!​

Answer 1

$\it Not\breve am\ \dfrac{1}{x+y}=a;\ \ \ \dfrac{1}{x-y}=b,\ \ iar\ sistemul\ devine:\\ \\ \\ \begin{cases} \it 6a+2b=4\Big|_{:2}\\ \\ \it 4a-b=\dfrac{1}{3}\end{cases} \Rightarrow \begin{cases} \it 3a+b=2\\ \\ \it 4a-b=\dfrac{1}{3}\end{cases} \stackrel{(+)}{\Longrightarrow} 7a=2\dfrac{1}{3} \Rightarrow\\ \\ \\ \Rightarrow 7a=\dfrac{7}{3} \Rightarrow a=\dfrac{7}{3}:7=\dfrac{7}{3}:\dfrac{7}{1}=\dfrac{7}{3}\cdot\dfrac{1}{7}\ \Rightarrow a=\dfrac{1}{3}$

$\it 3a+b=2 \Rightarrow 3\cdot\dfrac{1}{3}+b=2 \Rightarrow 1+b=2 \Rightarrow b=1\\ \\ \\ Revenim\ asupra\ nota\c{\it t}iei:\\ \\ \\ a=\dfrac{1}{3} \Rightarrow \dfrac{1}{x+y}=\dfrac{1}{3} \Rightarrow x+y=3;\\ \\ \\ b=1 \Rightarrow \dfrac{1}{x-y}=1 \Rightarrow x-y=1$

$\it Sistemul\ \ devine:\ \begin{cases} \it x+y=3\\ \\ \it x-y=1\end{cases} \Rightarrow x=2,\ \ y=1$