Y=MAX((3x+y),(11x-y)) then what's the value of y?

For the condition that
  (3x+y) > (11x - y),
we have
  2y > 8x
  y > 4x
Under this condition,
  y = 3x + y
  0 = 3x
  0 = x  and  y > 0

For the opposite condition
  (3x + y) < (11x - y)
  y < 4x
And
  y = 11x - y
  2y = 11x
  y = (11/2)x

Using this value for y in the relation with x, we have
  (11/2)x < 4x
  (3/2)x < 0
  x < 0

When x = 0, the value of y is any non-negative number
When x < 0, the value of y is (11/2)x.

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There are no solutions to the equation when x > 0.