Given that 2Y + 2Z of x = 2x + 2Z of y = 2x + 2Y of Z = k, find the value of K

Given that 2Y + 2Z of x = 2x + 2Z of y = 2x + 2Y of Z = k, find the value of K

2Y + 2Z / x = 2x + 2Z / y = 2x + 2Y / z = k2y + 2Z = KX 2x + 2Z = KY 2x + 2Y = KZ: 4 (x + y + Z) = K (x + y + Z) k = 4

(2x + y) / z = (2Y + Z) / x = (2Z + x) / 7 = k, find K

(2x + y) / z = (2Y + Z) / x = (2Z + x) / y = k, find K
Is the denominator 7 y, and if it is y
So, x = y = Z, and K = 3

If (x + y) / 2x = (Z + x) / 2Y = (x + y) / 2Z = k, then the value of K is

It is known that, (y + Z) / 2x = (Z + x) / 2Y = (x + y) / 2Z = K,
We can get: y + Z = 2kx, Z + x = 2ky, x + y = 2kZ,
The sum of the three formulas is: 2 (x + y + Z) = 2K (x + y + Z),
The results are as follows: 2 (k-1) (x + y + Z) = 0,
The equation holds for any x, y, Z,
Then k-1 = 0,
The solution is k = 1