  We have embedded an AlGaAs/GaAs based, gated 2D hole system (2DHS) into an
impedance transformer $LC$ circuit, and show that by using radio-frequency
reflectometry it is possible to perform sensitive, large bandwidth, electrical
resistance measurements of 2D systems at mK temperatures. We construct a simple
lumped element model where the gated 2DHS is described as a resistive
transmission line. The model gives a qualitative understanding of the
experimental results. As an example, we use our method to map out the Landau
level evolution in a 2DHS as a function of magnetic field and gate voltage.
