Question

resolva os sistemas: x+y=7
                                       x.y=10
 

Answer 1

$\left \{ {{x+y=7} \atop {xy=10}} \right.$

x = 7-y
y(7 - y) =10
7y - 2y = 10
5y = 10
y = 2

x+2 = 7
x= 7-2
x= 5

Answer 2

{x + y = 7
{xy = 10

x + y = 7
x = 7 - y

xy = 10
(7 - y)*y = 10
-y² + 7y = 10 .(-1)
y² - 7y = -10
y² - 7y + 10 = 0

Δ = (-7)² - 4 * 1 * 10
Δ = 49 - 40
Δ = 9

y' = -b + √Δ / 2a
y' = -(-7) + √9 / 2
y' = 7 + 3 / 2
y' = 10 / 2
y' = 5

y" = 7 - 3 / 2
y" = 4 / 2
y'' = 2

substituindo com y = 5

x = 7 - y
x = 7 - 5
x = 2

substituindo com y = 2

x = 7 - y
x = 7 - 2
x = 5

R ⇒ x = 2 e y = 5 ou x = 5 e y = 2