Your Ti-89 should retain 11 equations in the Numeric Solver. I believe you should be able to delete the specific variable name and that should delete the equation. As you edit and add equations, the oldest equation will drop off the list too. If you have the list of 11 equations from the numeric screen (F5), toggle to that equation and delete (not sure of this, but should work and be the most efficient).
Thanks for the question, I never bothered to worry about this as I just entered new equations and let the calculator just add and drop the old equations off. This is not efficient by any means, but I don't use my Ti-89 all that much, so I didn't realize I only had 11 equations available.
One suggestion, not sure if practical or even possible: I had suspected I may need to insert equations as comments in a BASIC program and pick and save into the solver. Awkward, but it would provide for more than 11 equations and in a convoluted file sort of way (different program names for different families of equations). I will dig into this over the weekend and provide an updated answer if any of the above is wrong or not feasible.
If you need more than 11 equations; for reference let us know how you accomplish?