Question

Решите методом сложения.​

Answer 1

Ответ:

$\left\{\begin{array}{l}\dfrac{9}{x+4y}-\dfrac{6}{5x-y}=-2\\\dfrac{3}{x+4y}+\dfrac{18}{5x-y}=1\end{array}\right\ \ \left\{\begin{array}{l}p=\dfrac{1}{x+4y}\\q=\dfrac{1}{5x-y}\end{array}\right\ \ \left\{\begin{array}{l}9p-6q=-2\ |\cdot 3\\3p+18q=1\end{array}\right\ \oplus$

$\left\{\begin{array}{l}30p=-5\\18q=1-3p\end{array}\right\ \ \left\{\begin{array}{l}p=-\dfrac{1}{6}\\18q=1+\dfrac{3}{6}\end{array}\right\ \ \left\{\begin{array}{l}p=-\dfrac{1}{6}\\18q=\dfrac{3}{2}\end{array}\right\ \ \left\{\begin{array}{l}p=-\dfrac{1}{6}\\q=\dfrac{1}{12}\end{array}\right$

$\left\{\begin{array}{l}\dfrac{1}{x+4y}=-\dfrac{1}{6}\\\dfrac{1}{5x-y}=\dfrac{1}{12} \end{array}\right\ \ \left\{\begin{array}{l}x+4y=-6\\5x-y=12\ |\cdot 4\end{array}\right\ \oplus\ \left\{\begin{array}{l}4y=-6-x\\21x=42\end{array}\right\ \ \left\{\begin{array}{l}4y=-8\\x=2\end{array}\right\\\\\\\left\{\begin{array}{l}y=-2\\x=2\end{array}\right\ \ \ \ \ Otvet:\ (2;-2)\ .$