Question

O Valor de y no sistema { x . y = 10 { x + y = 7 . O valor do par ordenado (X, Y) é:
a) (3, 4 )
b) (1 , 6)
c) ( 5, 5)
d) (5, 2)

Answer 1

X.Y = 10
X + Y = 7
X = 7 - Y
substitui x
x.y = 10
(7 - y ) . y = 10
-y² + 7 y = 10
-y² + 7 y - 10 = 0
Δ = b² - 4.a.c
Δ = 7² - 4 . -1 . -10
Δ = 49 - 40
Δ = 9 ⇒ √ 9 = 3
x = - b + ou - 3 / 2. - 1
x´= -7 + 3 / -2
x´= -4 / -2 = 2
x´´ = -7 - 3 / - 2
x´´= -10 / - 2 = 5
x = 5
x.y = 10
5.y = 10
y = 10/5
y = 2
(x,y) = (5,2)

x= 2
x.y = 10
2 y = 10
y = 10/2
y = 5
(x,y) = (2,5)

Resposta letra d) (5,2)