Question

Розв'язати систему рівнянь: (x - 1) ^ 2 - (x + 2) ^ 2 = 3y ,\\ (y-3)^ 2 -(y+2)^ 2 =5x. помогите срочно даю 100 баллов!!!​

Answer 1

$\displaystyle\bf\\\left \{ {{(x-1)^{2}-(x+2)^{2} =3y } \atop {(y-3)^{2} -(y+2)^{2} =5x}} \right. \\\\\\\left \{ {{(x-1-x-2)\cdot(x-1+x+2)=3y} \atop {(y-3-y-2)\cdot(y-3+y+2)=5x}} \right.\\\\\\\left \{ {{-3\cdot(2x+1)=3y \ |:(-3)} \atop {-5\cdot(2y-1)=5x \ |:(-5)}} \right. \\\\\\\left \{ {{2x+1=-y} \atop {2y-1=-x}} \right. \\\\\\\left \{ {{2x+y=-1 \ |\cdot (-2)} \atop {x+2y=1 }} \right. \\\\\\+\left \{ {{-4x-2y=2} \atop {x+2y=1}} \right. \\----------\\-3x=3\\\\x=3:(-3)=-1$

$\displaystyle\bf\\y=-2x-1=-2\cdot(-1)-1=2-1=1\\\\\\Otvet \ : \ (-1 \ ; \ 1)$