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An injection-locked laser system where the master laser is directly modulated is analyzed using rate equations. Both quasi-static and dynamic analyses are carried out in order to ensure that the parameters lie inside the locking range. The analysis is valid for all injection levels. The quasi-static analysis provides a good basis for explaining the phenomena. It is shown that, for a given detuning frequency, maximum suppression of intensity modulation (IM) occurs at a specific value of the injection ratio. At low frequencies, the frequency modulation (FM) index of the slave laser bears a constant ratio to the FM index of the master laser of less than unity. It is illustrated that the direct FM scheme is only viable for modulation frequencies up to about 100 MHz. Large IM suppression can only be achieved for large values of the linewidth enhancement factor of the slave laser, small magnitude of the detuning frequency, and low injection ratio. The latter two conditions are associated with narrow limits on stable operation, and care should be taken to avoid instability.