Question

(Pref. Telesópolis) Se 2x-y=1, 2y-z=2 e 2z-x=3, qual valor de x+y+z?

Answer 1

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