Question

Se 2x - y = 1, 2y - z = 2 e 2z - x = 3, qual é o valor de x + y + z ?

Answer 1

Resposta: 6

Explicação passo a passo:

2 x - y = 1

2 y - y = 2

2 z - x = 3

2 x - y = 1

x = (1 + y)/2

2 z - x = 3

2 z - (1 + y ) /2 =3

m.m.c = 2

4 z / 2 - (1 + y )/2 = 6/2 eliminar o denominador

4 z - 1 - y = 6

4 z = 6 + 1 + y

4 z = 7 + y

z = (7 + y) / 4

2 y - z = 2

2 y - (7 + y ) / 4 = 2

m.m.c = 4

8 y / 4 - (7 + y ) / 4 = 8/4 eliminar o denominador

8 y - 7 - y = 8

7 y = 8 + 7

7 y = 15

y = 15/7

z = (7 + y) /4

z = (7 + 15/7) / 4

z = (49/7 + 15/7) / 4

z = 64/7 / 4

z = 64/7 x 1/4

z = 16/7

x = (1 + y) / 2

x = (1 + 15/7) / 2

x = (7/7 + 15/7 ) / 2

x = 22/7 x 1/2

x = 11/7

x + y + z =

11/7 15/7 + 16/7 =

42/7 = 6