Question

Resolva os seguintes sistemas lineares:
a)

x-y+2z=1

-2x+2y-4z=-2

x+y-z=5

b)

x+2y+z+w=3

x+y+2z+w=7

x+y+z+2w=9

2x+y+z+w=5

Answer 1

Resposta: R: X = -1 / Y = 0 / W = 2 / Z = 1

Explicação passo-a-passo:

Somando-se os termos :

2X + Y + Z + W = 1

X + 2Y + Z + W = 2

X + Y + 2Z + W = 3

X + Y + Z + 2W = 4

_______________________

5X +5Y + 5Z +5 W = 10

Então para simplificar nosso trabalho fiz :

\frac{5X +5Y + 5Z +5 W = 10}{5} = X + Y + Z + W = 2

Então eu fui montando sistemas:

1-

2X + Y + Z + W = 1

X + Y + Z + W = 2 .(-1)

2X + Y + Z + W = 1

-X - Y - Z - W =- 2

_______________

X= -1

2-

X + 2Y + Z + W = 2

X + Y + Z + W = 2 .(-1)

X + 2Y + Z + W = 2

-X - Y - Z - W =- 2

___________________

Y = 0

3-

X + Y + 2Z + W = 3

X + Y + Z + W = 2 .(-1)

X + Y + 2Z + W = 3

-X - Y - Z - W =- 2

__________________

Z = 1

4-

X + Y + Z + 2W = 4

X + Y + Z + W = 2 .(-1)

X + Y + Z + 2W = 4

-X - Y - Z - W =- 2

__________________

W = 2

R: X = -1 / Y = 0 / W = 2 / Z = 1