Question

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Answer 1

Explicação passo-a-passo:

a)

3x + y = 1

x - y = -1

3 1

1 -1

D = 3 . (-1) - (1 . 1)

D = -3 - (1)

D = -4

1 1

-1 -1

Dx = 1 . (-1) - (-1 . 1)

Dx = -1 - (-1)

Dx = 0

x = Dx/D = 0/-4 = 0

3 1

1 -1

Dy = 3 . (-1) - ( 1 . 1)

Dy = -3 -(1)

Dy = -4

y = Dy/D = -4/-4 = 1

S = {(0, 1)}

b)

2x - y = 5

5x - 2y = 13

2 -1

5 -2

D = 2 . (-2) - (5 . (-1))

D = -4 - (-5)

D = 1

5 -1

13 -2

Dx = 5 . (-2) - (13 . (-1))

Dx = -10 - (-13)

Dx = 3

x = Dx/D = 3/1 = 3

2 5

5 13

Dy = 2 . 13 - ( 5 . 5)

Dy = 26 -(25)

Dy = 1

y = Dy/D = 1/1 = 1

S = {(3, 1)}

c)

4x + 3y = 8

2x - 5y = 30

4 3

2 -5

D = 4 . (-5) - (2 . 3)

D = -20 - (6)

D = -26

8 3

30 -5

Dx = 8 . (-5) - (30 . 3)

Dx = -40 - (90)

Dx = -130

x = Dx/D = -130/-26 = 5

4 8

2 30

Dy = 4 . 30 - ( 2 . 8)

Dy = 120 -(16)

Dy = 104

y = Dy/D = 104/-26 = -4

S = {(5, -4)}

d)

x + 2y = -5

3x - y = -1

1 2

3 -1

D = 1 . (-1) - (3 . 2)

D = -1 - (6)

D = -7

-5 2

-1 -1

Dx = -5 . (-1) - (-1 . 2)

Dx = 5 - (-2)

Dx = 7

x = Dx/D = 7/-7 = -1

1 -5

3 -1

Dy = 1 . (-1) - ( 3 . (-5))

Dy = -1 -(-15)

Dy = 14

y = Dy/D = 14/-7 = -2

S = {(-1, -2)}