Question

система y+4x=6
x^2+3xy-y^2=3

Answer 1

y=6-4x
x²+3x*(6-4x)-(6-4x)²-3=0
x²+18x-12x²-36+48x-16x²-3=0
-27x²+66x-39=0 /:(-3)
9x²-22x+13=0
D=484-468=16
x1=(22-4)/18=1⇒y1=6-4*1=6-4=2
x2=(22+4)/18=13/9⇒y2=6-4*13/9=(54-52)/9=2/9
Ответ (1;2);(13/9;2/9)

Answer 2

$left { {{y+4x=6} atop {x^2+3xy-y^2=3}} right. Rightarrow left { {{y=6-4x} atop {x^2+3x(6-4x)-(6-4x)^2=3}} right. Rightarrow \ Rightarrowleft { {{y=6-4x} atop {x^2+18x-12x^2-36+48x-16x^2-3=0}} right. Rightarrow \ Rightarrow left { {{y=6-4x} atop {27x^2-66x+39=0}} right. Rightarrow left { {{y=6-4x} atop {9x^2-22x+13=0}} right. Rightarrow \ Rightarrow left { {{y=6-4x} atop {x= frac{22б 4 }{18} }} right.$
$left { {{y=6-4x} atop {x= frac{11б2}{9} }} right. Rightarrow \ left { {{x= frac{13 }{9} } atop {y=6- frac{52 }{9} =frac{2 }{9} }} right. or left { {{x= 1 } atop {y=6- 4= 2 } right.$

Answer 3

D₁ =11² -9*13 =2² , x =(11 ± 2) /9