Question

Решить методом замены переменных​
пожалуйста, очень срочно нужно.

Answer 1

$\displaystyle\bf\\3(x-y)-2(x-y)^{2} =-2\\\\x-y=m\\\\3m-2m^{2}+2=0\\\\2m^{2} -3m-2=0\\\\D=(-3)^{2}-4\cdot 2\cdot (-2)=9+16=25=5^{2} \\\\m_{1} =\frac{3-5}{4} =-0,5\\\\m_{2} =\frac{3+5}{4} =2$

$\displaystyle\bf\\1)\\\\\left \{ {{x-y=-0,5}|\cdot7 \atop {2x+7y=-5}} \right.\\\\\\+\left \{ {{7x-7y=-3,5} \atop {2x+7y=-5}} \right.\\----------\\ 9x=-8,5\\\\x=-\frac{17}{18} \\\\y=x+0,5=-\frac{17}{18} +\frac{1}{2} =-\frac{8}{18} =-\frac{4}{9} \\\\\boxed{\Big(-\frac{17}{18} \ ; \ -\frac{4}{9}\Big )}\\\\\\2)\\\\\left \{ {{x-y=2}|\cdot7 \atop {2x+7y=-5}} \right. \\\\\\+\left \{ {{7x-7y=14} \atop {2x+7y=-5}} \right. \\----------\\9x=9\\\\x=1\\\\y=x-2=1-2=-1$

$\displaystyle\bf\\ \boxed{(1 \ ; \ - 1)}\\\\Otvet:\Big(-\frac{17}{18} \ ; \ -\frac{4}{9} \Big) \ , \ \Big(1 \ ; \ -1\Big)$