Under the conditions that the maximum of the expression is 3x+y, we have

3x + y > 11x - y

2y > 8x

y > 4x

and

y = 3x + y

0 = 3x

x = 0

Under the conditions that the maximum of the expression is 11x-y, we have

3x + y < 11x -y

y < 4x

and

y = 11x - y

2y = 11x

y = 5.5x

or

5.5x < 4x

1.5x < 0

x < 0

There is no solution for x > 0.

3x + y > 11x - y

2y > 8x

y > 4x

and

y = 3x + y

0 = 3x

x = 0

**For x=0, y can be any positive number.**Under the conditions that the maximum of the expression is 11x-y, we have

3x + y < 11x -y

y < 4x

and

y = 11x - y

2y = 11x

y = 5.5x

or

5.5x < 4x

1.5x < 0

x < 0

**For x < 0, y = 5.5x**

A graph of this equation will be a (half) line of slope 5.5 to the left of x=0, and a (half) line x=0 above the x-axis.There is no solution for x > 0.