Question

Resolva os Sistemas:

Answer 1

2)
a)
x - y = 7   x = 7 + y
   xy = 60

x.y = 60
(7 + y).y = 60
7y + y² = 60
y² + 7y - 60 = 0

a = 1; b = 7, c = - 60

Δ = b² - 4ac
Δ = 49 - 4.1.(- 60)
Δ = 49 + 240
Δ = 289
√Δ = 17

x = - b +/- √Δ
         2a

x = - 7 + 17 = 10/2 = 5
          2
x = - 7 - 17 = - 24/2 = - 12
         2

x = 5
xy = 60
5y = 60 y = 60/5 = 12

x = - 12
-12y = 60
y = 60: (-12); y = - 5

b) x² + y² = 20  
    x + y = 6     

x = 6 - y

(6 - y)² + y² = 20
36 - 12y + y² + y² = 20
2y² - 12y + 36 - 20 = 0
2y² - 12y + 16 = 0 (:2)
y² - 6y + 8 = 0

a = 1, b =  - 6, c = 8

Δ = b² - 4ac
Δ = 36 - 4.1.8
Δ = 36 - 32
Δ = 4

x = - b +/- √Δ
             2a

x = 6 + 2 = 8/2 = 4
        2

x = 6 - 2 = 4 /2 = 2
        2

x = 4
x + y = 6
4 + y = 6
y = 6 - 4
y = 2

x = 2
x + y = 6
2 + y = 6
y = 6 - 2
y = 4

c)
Método da Adição:

x² + y² = 13
x² - y² = 5   (+)

2x² = 18
x² = 18/2
x = √9
x = +/- 3

x² + y² = 13
3² + y² = 13
9 + y² = 13
y² = 13 - 9
y² = 4
y = +/-  2

d)
x + y = 10                x = 10 - y
x + y = 52 - 2xy

x = 10 - y

     x   + y = 52 - 2xy
10 - y + y = 52 - 2.(10 - y).y
10 = 52 - 2y (10 - y)
10 - 52 = - 20y + 2y²
- 42 = - 20y + 2y²
2y² - 20y = - 42
2y² - 20y + 42 = 0
y² - 10y + 21 = 0

a = 1, b = - 10, c = 21

Δ = b² - 4ac
Δ = 100 - 4.1.21
Δ = 100 - 84
Δ =  16

x = - b +/- √Δ
          2a

x = 10 + 4 = 14/2 = 7
         2

x = 10 - 4 = 6/2 = 3
        2

x = 3
x + y = 10
3 + y = 10
y = 10 - 3
y = 7

x = 7
x + y = 10
7 + y = 10
y = 10 - 7
y = 3