  We prove low-regularity global well-posedness for the 1d Zakharov system and
3d Klein-Gordon-Schr\"odinger system, which are systems in two variables
$u:\mathbb{R}_x^d\times \mathbb{R}_t \to \mathbb{C}$ and
$n:\mathbb{R}^d_x\times \mathbb{R}_t\to \mathbb{R}$. The Zakharov system is
known to be locally well-posed in $(u,n)\in L^2\times H^{-1/2}$ and the
Klein-Gordon-Schr\"odinger system is known to be locally well-posed in
$(u,n)\in L^2\times L^2$. Here, we show that the Zakharov and
Klein-Gordon-Schr\"odinger systems are globally well-posed in these spaces,
respectively, by using an available conservation law for the $L^2$ norm of $u$
and controlling the growth of $n$ via the estimates in the local theory.
