Abstract: Strength is a fundamental invariant for forms (homogeneous polynomials) of fixed degree in many variables, with both geometric and arithmetic applications. Over algebraically closed fields, forms of high strength have various desirable geometric properties. In arithmetic applications (non-closed fields), it's therefore of considerable interest to bound the strength of a polynomial in terms of its strength over the algebraic closure. We will present a linear bound over Q, proving a special case of a conjecture of Adiprasito, Kazhdan and Ziegler. In the course of the proof, we obtain a stronger result on rational solutions to systems of multi-linear equations, which may be of independent interest.