Question

Determine, em R, o conjunto solução do sistema: {x-y=2 {x+y^2=4

Answer 1

$\begin{cases}x-y=2 ~~---\ \textgreater \ (I)\\ \\ x+y\²=4~~---\ \textgreater \ (II)\end{cases} \\ \\ substraindo~(II)-(I) \\ \\ \begin{cases}~~~x+y\²=4 \\ \underline{-x+y=-2~}\end{cases}\\ ~~~~~~ y\²+y=2 \\ y\²+y-2=0~~=\ \textgreater \ (y+2)(y-1)=0~~\begin{cases}y=-2 \\ y=1\end{cases} \\ \\ Entao, em~(I)~achamos~x \\ x-1=2 ~=\ \textgreater \ \boxed{x=3 }\\ x-(-2)=2~=\ \textgreater \ \boxed{x=0 }$