Question

RESOLVA OS SISTEMAS LINEARES

A)
x + y = 11
4x - 3y = 23

B)
3x + 4y - 7
5x + 3y = 19

C)
x + y + z = 8
2x - 3y + 2z = 21
x + 2y - z = -1 ​

Answer 1

Explicação passo-a-passo:

A)

x + 1y = 11

4x - 3y = 23

1y = 11 - 1x

y = (11 - 1x)/(1)

4x - 3(11 - 1x)/(1) = 23

4x + (-33 + 3x)/(1) = 23

4x - 33 + 3x = 23

7x = 56

x = 8

y = (11 -1 . 8) / 1

y = (11 - 8) / 1

y = 3/1

y = 3

B)

3x + 4y = 7

5x + 3y = 19

4y = 7 - 3x

y = (7 - 3x)/(4)

5x + 3(7 - 3x)/(4) = 19

5x + (21 - 9x)/(4) = 19

20x + 21 - 9x = 76

11x = 55

x = 5

y = (7 -3 . 5) / 4

y = (7 - 15) / 4

y = -8/4

y = -2

C)

1 1 1 8

2 -3 2 21

1 2 -1 -1

D = 3 + 2 + 4 + 3 - 4 + 2

D = 10

8 1 1

21 -3 2

-1 2 -1

Dx = 24 - 2 + 42 - 3 - 32 + 21

x = Dx/D = 5

1 8 1

2 21 2

1 -1 -1

Dy = -21 + 16 - 2 - 21 + 2 + 16

y = Dy/D = -1

1 1 8

2 -3 21

1 2 -1

Dz = 3 + 21 + 32 + 24 - 42 + 2

z = Dz/D = 4