  We investigated the theoretical possibility of accurately determining the
helium-to-metal enrichment ratio $\Delta Y/\Delta Z$ from precise observations
of double lined eclipsing binary systems. Using Monte Carlo simulations, we
drew synthetic binary systems with masses between 0.85 and 1.00 $M_{\odot}$
from a grid of stellar models with $\Delta Y/\Delta Z = 2.0$ [...].
Subsequently, a broader grid with $\Delta Y/\Delta Z$ from 1.0 to 3.0 was used
in the fitting process. To account for observational uncertainties, two
scenarios were explored: S1 with realistic uncertainties of 100 K in
temperature and 0.1 dex in [Fe/H], and S2 with halved uncertainties. We
repeated the simulation at two baseline metallicities: [Fe/H] = 0.0 and -0.3.
The posterior distributions of $\Delta Y/\Delta Z$ were severely biased towards
the edge of the allowable range in the S1 errors scenario. The situation only
marginally improved when considering the S2 scenario. The effect is due to the
impact of changing $\Delta Y/\Delta Z$ in the stellar effective temperature and
its interplay with [Fe/H] observational error, and it is therefore not
restricted to the specific fitting method. Despite the presence of these
systematic discrepancies, the age of the systems were recovered unbiased with
10% precision. Our findings indicate that the observational uncertainty in
effective temperature and metallicity significantly hinders the accurate
determination of the $\Delta Y/\Delta Z$ parameter from main sequence binary
systems.
