Question

помогите решить систему уравнений​

Answer 1

$\displaystyle \begin{cases}</p><p>\displaystyle \frac{1}{x+y} - \frac{6}{x-y} = -2 \\\\ \displaystyle</p><p>\frac{1}{x+y} + \frac{3}{x-y} = \frac{1}{4}</p><p>\displaystyle \end{cases} \\\\</p><p> ---------\\\\</p><p></p><p>\displaystyle \frac{1}{x+y} = t \; \; , \; \; \frac{1}{x-y} = u \\\\</p><p></p><p>\displaystyle \begin{cases}</p><p>\displaystyle t-6u=-2 \\\\ \displaystyle</p><p>\displaystyle t+3u=\frac{1}{4} \; \; \mid \; \; \cdot (-1)</p><p>\displaystyle \end{cases} \\\\</p><p></p><p>\displaystyle \begin{cases}</p><p>\displaystyle t-6u=-2 \\\\ \displaystyle</p><p>\displaystyle -t-3u=-\frac{1}{4}</p><p>\displaystyle \end{cases} \\\\</p><p></p><p>\displaystyle -9u=-\frac{9}{4} \;\; \mid \; \; \div (-9) \\\\</p><p>\displaystyle u=\frac{1}{4} \\\\</p><p></p><p>--------\\\\</p><p></p><p>\displaystyle t + 3u = \frac{1}{4}\\\\</p><p>\displaystyle t+3\cdot \frac{1}{4} = \frac{1}{4} \\\\</p><p>\displaystyle t = -\frac{1}{2} \\\\</p><p></p><p>--------\\\\</p><p> </p><p> \displaystyle \begin{cases}</p><p>\displaystyle -\frac{1}{2} - 6\cdot \frac{1}{4}=-2 \\\\ \displaystyle</p><p>-\frac{1}{2}+3\cdot \frac{1}{4}=\frac{1}{4}</p><p>\displaystyle \end{cases} \\\\</p><p></p><p>\displaystyle \begin{cases}</p><p>\displaystyle -2 = -2 \\\\ \displaystyle</p><p>\frac{1}{4} = \frac{1}{4}</p><p>\displaystyle \end{cases} \\\\ </p><p>- - - - - - - -\\\\</p><p>\displaystyle \begin{cases}</p><p>\displaystyle \frac{1}{x+y} = -\frac{1}{2} \\</p><p>\displaystyle \frac{1}{x-y} = \frac{1}{4} </p><p>\displaystyle \end{cases} \\\\</p><p></p><p>\displaystyle x = 1 \;\; , \; \; y = -3 \\\\</p><p>----------\\\\ </p><p></p><p>\displaystyle \begin{cases}</p><p>\displaystyle \frac{1}{1-3} - \frac{6}{1-(-3)} = -2 \\\\</p><p>\displaystyle \frac{1}{1-3} + \frac{3}{1-(-3)} = \frac{1}{4} </p><p>\displaystyle \end{cases} \\\\</p><p></p><p>\displaystyle \begin{cases}</p><p>\displaystyle -2 = -2 \\\\ \displaystyle</p><p>\frac{1}{4} = \frac{1}{4}</p><p>\displaystyle \end{cases} \\\\\\</p><p>----------\\\\\\</p><p>\displaystyle \huge \boxed{x=1 \; \; , \; \; y=-3}$