  In cavity magnomechanical systems, magnetic excitations couple simultaneously
with mechanical vibrations and microwaves, combining the tunability of the
magnetization, the long lifetimes of mechanical modes and the whole measurement
toolbox of microwave systems. Such hybrid systems have been proposed for
applications ranging from thermometry to entanglement generation. However,
backaction noise can hinder the measurement of the mechanical vibrations,
potentially rendering such applications infeasible. In this paper, we
investigate the noise introduced in a mechanical mode of a cavity
magnomechanical system in a one-tone drive scheme and propose a scheme for
realizing backaction evasion measurements of the mechanical vibrations. Our
proposal consists of driving the microwave cavity with two tones separated by
twice the phonon frequency and with amplitudes balanced to generate equal
numbers of coherent magnons. We demonstrate that different configurations of
such a scheme are possible and show that drives centered around the lower
frequency magnon-microwave polariton in a triple resonance scheme add the
minimum imprecision noise in the measurement, even though such configuration is
not the most robust to imperfections.
