1)
![\left \{ {{x-y=2} \atop {(x-y)(x+y)=8}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7Bx-y%3D2%7D+%5Catop+%7B%28x-y%29%28x%2By%29%3D8%7D%7D+%5Cright.+)
![\left \{ {{x=2+y} \atop {2(x+y)=8}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7Bx%3D2%2By%7D+%5Catop+%7B2%28x%2By%29%3D8%7D%7D+%5Cright.+)
![\left \{ {{x=2+y} \atop {x+y=4}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7Bx%3D2%2By%7D+%5Catop+%7Bx%2By%3D4%7D%7D+%5Cright.+)
![\left \{ {{2+y+y=4} \atop {x=2+y}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B2%2By%2By%3D4%7D+%5Catop+%7Bx%3D2%2By%7D%7D+%5Cright.+)
![\left \{ {{2y=2} \atop {x=2+y}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B2y%3D2%7D+%5Catop+%7Bx%3D2%2By%7D%7D+%5Cright.+)
![\left \{ {{y=1} \atop {x=3}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7By%3D1%7D+%5Catop+%7Bx%3D3%7D%7D+%5Cright.+)
Ответ: (3;1)
2)
![\left \{ {{ x^{2} + y^{2}-2x+3y=31} \atop { x^{2} +y ^{2}-2x-y =15}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B+x%5E%7B2%7D+%2B+y%5E%7B2%7D-2x%2B3y%3D31%7D+%5Catop+%7B+x%5E%7B2%7D+%2By+%5E%7B2%7D-2x-y+%3D15%7D%7D+%5Cright.+)
Вычитаем из первого уравнения системы второе уравнение, получаем:
3y+y=31-15
4y=16
y=4
Подставляем полученный у в первое уравнение системы:
![x^{2} -2x+16+12=31](https://tex.z-dn.net/?f=+x%5E%7B2%7D+-2x%2B16%2B12%3D31)
![x^{2} -2x-3=0](https://tex.z-dn.net/?f=+x%5E%7B2%7D+-2x-3%3D0)
x = -1
x = 3
Ответ: (-1;4) (3;4)
X≥2 U x≥-a⇒a≥-2
9(x-2)=(x+a)²
x²+2ax+a²-9x+18=0
x²+x(2a-9)+(a²+18)=0
D=(2a-9)²-4(a²+18)=4a²-36a+81-4a²-72=9-36a>0
36a<9
a<0,25
a∈[-2;0,25)
6/7=0,9(примерно)
0,7
7/6=1,2(примерно)
2/3=0,66=0,7(примерно)
наименьшее-2/3
{х-4у=7
{2х-у=7
{х=7=4у
{2х-у=7
2(7=4у)-у=7
х=3
(х,у)=(3,-1)
{3-4 *(-1)=7
{2*3-9-1)=7
{7=7
{7=7