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sistem de 2xy + 7x + 7y=25
x + y + xy=5


Răspuns :

2xy+7x+7y=25
xy+ x + y=5/(•-2)=>

2xy+7x+7y=25
-2xy-2x-2y=-10
____________+
2xy-2xy+7x-2x+7y-2y=25-10=>
5x+5y=15=>x+y=3=>x=3-y

Inlocuim in a doua relatie:
(3-y)y+(3-y)+y=5=>
3y-y^2+3-y+y=5=>
-y^2+3y+3=5=>
y^2-3y-3=-5=>
y^2-3y+2=0=>
y^2-2y-y+2=0=>
y(y-2)-1(y-2)=0=>
(y-1)(y-2)=0=>
y=1 sau y=2

x+y=3=>x+1=3 sau x+2=3=>
x=2 sau x=1

S={ (1; 2) ; (2;1) }

fie x+y=s
xy=p
atunci
2p+7s=25
p+s=5
2 ecuatii, 2 necunoscute metoda substitutiei
p=5-s
2(5-s) +7s=25
5s+10=25
5s=15
s=3
 p=5-s
p=2
x+y=3
xy=2
Construim ecuatia
u²-3u+2=0
u1=1
u2=2
x=1 ; y=2
x=2; y=1

S= {(1;2) ;(2;1)}