A load-changes-the-node scan attaches a load as a parallel branch across the bottom resistor, checking that the loaded node V_out,loaded falls below the unloaded value as the current splits at the node row by row. The arithmetic is exact only for the stated source voltages, resistances, load resistances, currents, output voltages, and rows in the ideal resistor, ideal supply, loaded model. Real dividers add resistor tolerance, source resistance, finite load impedance, input threshold spread, temperature drift, meter/probe calibration limits, finite precision, and measurement uncertainty.
A load resistor changes the divider because it becomes a real branch in the circuit topology. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
The load becomes a parallel branch
The bottom resistor and the load are both 6 ohm, so their parallel equivalent is 3 ohm.
Rlower loaded=3ohm
The output current splits exactly
The source current is 2 amperes. At the output node, it splits into 1 ampere through the bottom resistor and 1 ampere through the load.