
I'm worried about this for several reasons:
1) With both "kx" ad "k" in the both equations, along with some constants, I'm struggling with what the units could be. Do they match up?
2) Since your three variables and only two equations, I am not hopeful that there is a unique solution. As this is a "Real" problem, I suppose there is a chance.
3) Too bad. I get two solutions. Both have y = 0 and I'm guessing you don't like that.
Solution # 1 x = 245.449, k = 5.226, y = 0
Solution # 2 x = 39.880, k = 123.550, y = 0
This formulation has problems around x = 30.8 and x = 1.132. These are really practical limits for x as you have it. Notice how both "Solutions" are outside these limits.
The minimum value of 'y', given the constraints on x, occurs at x = 21.540 and is y = 371.072
Perhaps if you described what it was you were doing we may be able to find a way out of this swamp.