Resposta :

[tex]\boxed{\frac{x}{5}=\frac{y}{10}\rightarrow x=\frac{y}{2}}[/tex]
Substituindo em 
[tex] x^{2} +y^2=20 \\ (\frac{y}{2})^2+y^2=20 \\ \frac{y^2}{4}+y^2=20 \\ y^2+4y^2=80 \\ 5y^2=80 \\ y^2=16 \\ y=4[/tex]
x=2


  x =  y    ==>   x= 5y==> x = y
 5    10                10            2


x^2+y^2=20
(1/2y)^2 + y^2 = 20

1/4y^2 + y^2 = 20

y^2 + 4y^2 = 80
   5y^2 =80
     y^2 =16

   y =+/- 4

y1=4 ==> x1 = 4/2 ==>x1=2

y2=-4==>x2 = - 4/2==> x2= -  2

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