Question

resolva o sistema x+y=´5 e x.y=6

Answer 1

$\left \{ \bigg{x+y=5} \atop\bigg{x\cdot{y}=6}} \right.\\\\\\x = 5 - y\\\\\\(5-y)\cdot{y}=6\\-y^2+5y=6\\y^2-5y+6=0\\\\a=1\ \ \ \ \ b=-5\ \ \ \ \ c=6\\\\\triangle=b^2-4ac\\\\\triangle=(-5)^2-4\cdot(1)\cdot(6)\\\triangle=25-24\\\triangle=1\\\\\\y= \dfrac{-b \frac{+}{-} \sqrt{\triangle} }{2a}\\\\\\y= \dfrac{-(-5) \frac{+}{-} \sqrt{1} }{2}\\\\\\y= \dfrac{5 \frac{+}{-}1 }{2}\\\\\\y'= \dfrac{6}{2}\\\\\\y'=3\\\\\\y"= \dfrac{4}{2}\\\\\\y"=2\\\\\\Para\ y=2,\ temos\ x=3\ e\ para\ y=3,\ x=2$

Answer 2

É bem simples:
se
x + y = 5
então
y = 5 - x
Faça a mesma coisa com o outro:
x . y = 6
y = 6 / x
Agr temos dois valores para y. Junte eles:
y = 5 - x
y = 6 / x
5 - x = 6 / x
Resolva:
5 - x = 6 / x
5 - 2 = 6 / 2
3 = 3
x = 2
Achamos x, agr usamos ele pra achar y:
y = 5 - x
y = 5 - 2
y = 3
y = 6 / x
y = 6 / 2
y = 3
Pronto, x=2 e y=3.