Решите систему уравнений методом введения новых переменных:

Решите задачу:

$\left \{ {{ \frac{3}{x+y} + \frac{6}{x-y} =-1,} \atop { \frac{5}{x+y} + \frac{9}{x-y} =-2,}} \right. \; \; t=\frac{1}{x+y}\; ,\; \; p=\frac{1}{x-y}\\\\ \left \{ {{3t+6p=-1|*(-5)} \atop {5t+9p=-2|*3}} \right. ;\left \{ {{-15t-30p=5} \atop {15t+27p=-6}} \right. ; \left \{ {{-3p=-1} \atop {15t+27p=-6}} \right. \\\\b) \left \{ {{3t+6p=-1|*9} \atop {5t+9p=-2|*(-6)}} \right. ; \left \{ {{27t+54p=-9} \atop {-30t-54p=12}} \right. \left \{ {{27t+54p=-9} \atop {-3t=3}} \right. \\\\c)\left \{ {{-3p=-1} \atop {-3t=3}} \right. \; \left \{ {{p=\frac{1}{3}} \atop {t=-1}} \right. \\\\\frac{1}{x+y}=-1\; ,\; x+y=-1\\\\\frac{1}{x-y}=\frac{1}{3}\; ,\; \; x-y=3\\\\ \left \{ {{x+y=-1} \atop {x-y=3}} \right. \; \left \{ {{2x=2} \atop {2y=-4}} \right. \; \left \{ {{x=1} \atop {y=-2}} \right.$